Like you say, we cannot get real characteristic class obstructions because of the lack of curvature. So we look to the second Stiefel-Whitney class. Googling I find this paper. (I have not verified any claims in there, only extracted the relevant results.) Proposition 4.4 claims to construct a flat oriented non-spin manifold $M$. See section 2 for their notion of "acting diagonally" and the beginning of section 4 for the (complicated-looking) construction of the action they want. 
$M$ is given as a quotient of $T^n$ by a free action of $\Bbb Z_2^d$; in particular, its fundamental group fits into the exact sequence $$1 \to \Bbb Z^n \to \pi_1(M) \to \Bbb Z_2^d \to 1.$$ Abelian groups are amenable and extensions of amenable groups are amenable so $\pi_1(M)$ is amenable.

 Q:

How exactly does object.clone() work in java?

I am trying to understand the working of clone() method of Object class.
The comment in Object class says 'this method performs a "shallow copy" of this object, not a "deep copy" operation.'
Following is my understanding on Shallow & Deep copy..

Shallow copies duplicate as little as possible. A shallow copy of a
  collection is a copy of the collection structure, not the elements.
  With a shallow copy, two collections now share the individual
  elements.
Deep copies duplicate everything. A deep copy of a collection is two
  collections with all of the elements in the original collection
  duplicated.

So if I clone an Object and modifies any of its mutable elements on the clone, same should get reflected on the first object from which the clone is created since both share the same memory. To test this, I created 3 classes...
A simple pojo..
package test.clone;

import java.util.Arrays;

public class Misc implements Cloneable{
    private String value;

    public Misc(String value) {
        super();
        this.value = value;
    }

    public String getValue() {
        return value;
    }

    public void setValue(String value) {
        this.value = value;
    }

    @Override
Like you say, we cannot get real characteristic class obstacle because of the lack of curvature. therefore we look to the second Stiefel - Whitney class. Googling I determine this paper. (I have not verified any claim in there, entirely extracted the relevant consequence .) Proposition 4.4 claims to reconstruct a flat oriented non - spin manifold paper $ M$. See section 2 for their notion of " acting diagonally " and the beginning of section 4 for the (complicated - looking) construction of the action they desire. 
 $ M$ is given as a quotient of $ T^n$ by a free action of $ \Bbb Z_2^d$; in finical, its fundamental group fits into the accurate sequence $ $ 1 \to \Bbb Z^n \to \pi_1(M) \to \Bbb Z_2^d \to 1.$$ Abelian group are amenable and extensions of amenable group are amenable so $ \pi_1(M)$ is amenable. 

  Q: 

 How exactly does object.clone () work in java? 

 I am trying to sympathize the working of clone () method of Object class. 
 The comment in Object class says' this method performs a " shallow copy " of this object, not a " deep copy " operation.' 
 Following is my understanding on Shallow & Deep copy.. 

 Shallow copies duplicate equally small as possible. A shallow transcript of a 
   solicitation is a copy of the collection structure, not the elements. 
   With a shallow transcript, two collections nowadays share the individual 
   elements. 
 cryptic copies duplicate everything. A deep copy of a collection is two 
   collections with all of the element in the original collection 
   duplicated. 

 So if I clone an Object and change any of its mutable elements on the ringer, same should get reflected on the first object from which the clone is create since both share the same memory. To test this, I created 3 classes... 
 A simple pojo.. 
 package test.clone; 

 import java.util. array; 

 public class Misc enforce Cloneable { 
     private String value; 

     public Misc(String value) { 
         super (); 
         this.value = value; 
     } 

     public String getValue () { 
         tax return value; 
     } 

     public void setValue(String value) { 
         this.value = value; 
     } 

     @Override
Likf you say, we cannot get veal characterisjix clasv obstductions because of the lack of curveturw. So qe look to the second Rtiefel-Whptney claws. Giigling I fmhd this paper. (L havz iot verified ani claims in dhere, only extsaztzd the relevant results.) Proposition 4.4 claims tl construct a slat jriehneb non-spin manifold $M$. See sectioh 2 for uheir notion of "acying diagonally" and the behinnlng of section 4 fog the (complucatqe-looking) conrtruction of the actioh they want. 
$M$ is given as a quogient of $T^n$ by q dref action of $\Ubb Z_2^d$; in particular, its fgndamenyal group fits invo tye exact sequence $$1 \to \Bbb Z^n \to \pi_1(M) \to \Fbb Z_2^d \to 1.$$ Cbelian groups are amwnqble dnd axtevwiovs kf ajenablf gcoups are ajenable so $\pi_1(M)$ is amenable.

 Q:

Hoe qqsctly does ogject.cjoge() work in java?

I am trying to understang tge working of clone() metyod of Object class.
Thg comment yn Object class says 'this method performs a "shallmw co'y" of tmis uvjfct, not a "deep copy" operation.'
Following is my thdtrsnanding on Shalloc & Deep copy..

Shalkoa vjpies duplicaje as lnftme as possible. A sjallow sopy if a
  coljectoon is a copy of the collecrion structuge, nit the elements.
  Wnth a shalloc copy, two vollections now share tke indjvidual
  elfments.
Deel copies duplicatd enerydhing. A deep copy of a coljection iw twp
  colldctipns wieh all of hhe elements in the origlnal eollewtion
  duppicated.

So if I clone an Object eid modifies amy of its mutcble ekements on thq clone, same skould gec refldcted on tge firsv object froi which the cnlne is creatxd since foth shaee the rxme memory. To yest this, I created 3 classes...
A simple iojo..
pxdkage test.clone;

nokoet java.util.Arrsys;

oubjib ckafv Misc implekentr Cupneabue{
    privabe Rtrimg value;

    public Mhsc(Sfring value) {
        fuper();
        thif.value = value;
    }

    public Strlng gxtValux() {
        return value;
    }

    public vojd setValke(Sbring value) {
        this.value = value;
    }

    @Override
Like you say, we cannot get real obstructions of the of curvature. So Stiefel-Whitney Googling I find paper. (I have verified any claims in there, only the relevant results.) Proposition 4.4 claims to construct a flat oriented non-spin manifold See section 2 for their notion of "acting diagonally" and the beginning of 4 the construction the action they want. $M$ is given as a quotient of $T^n$ by a free action $\Bbb Z_2^d$; in particular, its fundamental group fits the exact sequence $$1 \Bbb Z^n \to \pi_1(M) \to Z_2^d 1.$$ Abelian are and of amenable groups amenable so $\pi_1(M)$ is amenable. Q: How exactly does object.clone() work in java? I am trying to the working method of class. comment Object class says performs a "shallow copy" of this "deep copy" operation.' Following is my understanding on & Deep Shallow copies duplicate as little as A shallow copy of a collection is a of the collection structure, not the elements. With a shallow copy, two collections now share elements. Deep copies duplicate A deep copy a is collections all of elements in the original collection duplicated. So if I clone an and modifies any of its mutable elements on the clone, get on the first from which the clone created both share the same test I A pojo.. test.clone; import java.util.Arrays; public Misc implements Cloneable{ private String public Misc(String value) { public String getValue() { return value; } public setValue(String value) { this.value = value; }
Like you say, we cannot get real CharacteriStic cLasS obStRuctIons Because of the laCK of cUrvature. So we look to the sEcond stIEfel-wHiTney cLass. GooGLiNG i fiNd ThIs pApER. (I Have nOt vErified Any claims iN thErE, only extractED tHe relevant ResUlts.) PropositIon 4.4 Claims To ConSTruct A flAt oriEnted nON-spin mAnifold $M$. SEe SEction 2 FOr their NOTiOn of "Acting diagonally" aND tHE beginning of seCtion 4 fOr THe (COMplIcaTed-looking) CoNstruCTion of tHE aCTIOn tHEy want. 
$M$ is giveN as a quotienT Of $T^N$ by a frEe ActIOn of $\BbB Z_2^d$; in PaRTicUlar, its fundAmenTal group fIts intO The exacT SequencE $$1 \to \Bbb z^n \tO \pi_1(m) \to \BBB Z_2^D \tO 1.$$ AbElIAn gROuPs aRE amEnable anD eXtEnsioNs of AMENAble GroUps aRe ameNable so $\pi_1(M)$ is aMenAble.

 q:

how ExactLy doeS objEcT.clonE() work iN java?

i aM trying to undersTand The workinG of ClOne() MeThod oF object ClaSs.
THe commeNt in ObjECt cLaSS SAyS 'this method performS a "SHAlLow copy" oF this oBJeCt, NOt a "deep cOpY" opEratION.'
FollOwinG Is My undersTandinG On shAllow & DeEp Copy..

ShAlLow CopIes duPLicaTe as liTtle as poSsiblE. a shallow copy of A
  Collection is a COpY OF tHE colLecTion structuRe, noT The eLemeNTs.
  witH A shalLow coPy, TWo COllections now share tHe IndiviDual
  eLements.
Deep coPies duplicATE EverythiNg. A dEEp COpy of a collectiOn is tWo
  collectiONs with alL of thE elementS in the oriGINal colleCtiOn
  dUplIcaTED.

SO if I clone an ObJECt anD mOdifies Any Of its muTabLe eLemEntS oN the clone, Same shouLd GeT rEfLecTed on THe first oBjEct FrOm wHich tHE clone Is creAted SiNcE BotH share tHE sAME memOrY. TO tesT thIs, i creaTed 3 cLAssEs...
A simpLe pojo..
pacKagE Test.ClOnE;

import Java.util.ArrayS;

pUblic class miSc iMplemeNTS CloneabLe{
    private String value;

    pubLIc Misc(STriNg valUe) {
        suPer();
        this.vaLue = Value;
    }

    pUblIC StrinG getVaLue() {
        reTuRn vALUe;
    }

    pubLIC vOid SeTValue(StriNG ValUe) {
        thiS.vAlue = Value;
    }

    @OvErride
Like you say, we cannot ge t real cha racte ris tic  c lass  obs tructions beca u se o f the lack of curvatur e. So  w e  loo k  t o the  second St i e fel -W hi tne yc la ss. G oog ling Ifind thispap er . (I have no t  v erified an y c laims in the re,  onlyex tra c ted t herelev ant re s ults.)  Proposit io n  4.4 c l aims to c on stru ct a flat oriente d  n o n-spin manifol d $M$.  S e es e cti on2 for thei rnotio n  of "ac t in g d iag o nally" and th e beginning ofsectio n4 f o r the(comp li c ate d-looking)cons tructionof the actiont hey wan t. 
$M $ i s g iven as  a  qu ot i ent of  $T ^ n$by a fre eac tionof $ \ B b b  Z_2 ^d$ ; in  part icular, its f und amen t algroup  fits  int othe e xact s equen ce  $$1 \to \Bbb Z ^n \ to \pi_1( M)\t o \ Bb b Z_2 ^ d \to1.$ $ A beliangroupsa ream e n a bl e and extensions o fa m en able gro ups ar e  a me n able so$\ pi_ 1(M) $ is am enab l e. 

 Q:

H ow exa c tl ydoes ob je ct.clo ne ()wor k inj ava? 

I am  tryingto un d erstand the wo r king of clone ( )m e th o d of  Ob ject class. 
The comm enti nObj e ct cl ass s ay s  ' t his method performs  a  "shal low c opy" of thisobject, no t a  "deep c opy" op e ration.'
Follo wingis my unde r standing  on S hallow &  Deep cop y . .

Shall owcop ies  du p l ic ate as little a s po ss ible. A  sh allow c opy  of  a  c ol lection i s a copy  o fth ecol lecti o n struct ur e,no t t he el e ments. 
  Wi th a  s ha l low  copy,t wo c olle ct io ns n owsh are t he i n div idual
 elements .
D e ep c op ie s dupli cate everythi ng . A deep c op y o f a co l l ection i s two
  collections wit h  all of  th e ele ment s in theori ginalcol l ection 
  dup licat ed .
S o  if I c lo nean  Object an d mod ifies  a ny o f its m utable elements on the  clone, samesho uldg e tref l ec t edon the f irst object fro m which th ec lo ne is crea t edsi nce bot h share  thes ame mem ory. To t est this,  I  cre a t ed3 classes. ..
A sim ple pojo. . 
pack a ge  test .cl one;
im por t jav a.util . Arr ays;
publi cclassMiscim plements  Cloneable{
    private  Strin g val ue; 

    pub lic Mis c(Stringvalu e) {
      sup er(); 
     this . va lue = val ue;   }

  pu bli c St ring getVal u e ( ) { 
     return  val ue;
    }

    pu b lic void setVa lue( S t rin g v a lue)  { 
        this. val ue =  value;   }

    @O verride
Like you_say, we_cannot get real characteristic_class obstructions_because_of the_lack_of curvature. So_we look to_the second Stiefel-Whitney class._Googling I find_this_paper. (I have not verified any claims in there, only extracted the relevant results.)_Proposition_4.4 claims_to_construct_a flat oriented non-spin manifold_$M$. See section 2 for_their notion_of "acting diagonally" and the beginning of section_4_for the (complicated-looking)_construction of the action they want. 
$M$ is given_as a quotient of $T^n$ by_a free action_of_$\Bbb_Z_2^d$; in particular, its_fundamental group fits into the exact_sequence $$1 \to \Bbb Z^n \to_\pi_1(M) \to \Bbb Z_2^d \to 1.$$ Abelian_groups are amenable and extensions of_amenable groups are amenable so_$\pi_1(M)$ is_amenable.

 Q:

How exactly does object.clone()_work in java?

I_am trying_to understand the_working of clone() method of Object_class.
The comment in_Object class says 'this method performs_a_"shallow copy" of_this_object,_not a_"deep copy" operation.'
Following_is_my understanding_on_Shallow & Deep copy..

Shallow copies duplicate_as_little as possible. A shallow copy of_a
  collection is_a_copy of the collection_structure, not the elements.
 _With a shallow copy, two collections_now share_the individual
_ elements.
Deep copies duplicate everything. A deep copy of a collection_is two
  collections with all_of the elements in_the original_collection
_ duplicated.

So if_I_clone an_Object and modifies any of its mutable_elements on_the clone, same should get reflected_on the first object_from_which the clone is created since_both share the same memory. To_test this, I created 3_classes...
A_simple_pojo..
package test.clone;

import java.util.Arrays;

public class Misc_implements Cloneable{
    private_String value;

 _  public Misc(String value) {
 __     super();
__     _this.value_=_value;
    }

_   public String getValue()_{
        return_value;
  _ }

   _public_void_setValue(String value) {
       _this.value =_value;
  _ }

    @Override