systolic swatantrata

vibhedak jyaamiti mein, systolic swatantrata iss tathya koo sandarbhit karati haye kii bund remanian manifolds mein unake systolic aparivartakon kii parwah kiye binaa manmaane dhang seey chhoti matra hoe sakati haye.
arthaat, systolic aparivartaniya yaa systolic aparivartaniya key utpaad samanya roop seey saarvbhaumik (i.ee. vakrata-mukt) ack bund remanian manifold kii kull matra key liye nichali seemaaen.
systolic swatantrata kaa pataa pahali baar ack aaee mein mikhail gromov dwara lagaaya gayaa thaa.aich.aeye.aiss. 1992 mein preprint (joe antatah key roop mein dikhaai diyaa), aur ise aage mikhail kaatz, michael friedman aur anya logon dwara vikasit kiya gayaa thaa. gromov key avalokan koo vistrit roop seey bataaya gayaa thaa. systolic swatantrata kaa vistaar seey adhyayan karane vaale pahale prakashanon mein seey ack haye. 
systolic swatantrata key quantum truti sudhaar mein anuprayog hain. systolic swatantrata parr mukhya parinamon kaa sarvekshan karein.
udaaharan key liye.
jatil prakshepya tala manmaane dhang seey chhoti matra key remanian metricks koo sweekaar kartaa haye, jaise kii pratyek aavashyak satah cumm seey cumm 1 kshetra kii hoti haye. yahaan ack satah koo "aavashyak" kahaa jaataa haye yadi ise parivesh 4-manifold mein ack bindu taka anubandhit naheen kiya jaa sakata haye.
systolic baadha.
systolic swatantrata key vipareet systolic baadha haye, joe aavashyak manifold key liye gromov kii systolic asamaanta jaisi systolic asamaantaon kii upasthiti kii visheshta haye.

