a φ-operade

beejaganitam mariyu beejaganita topologylo operades siddhaantamlo, oka φ-operad anedi samaruupata pondikaina anubandhamgaa unde gunakaara pataniki oka paramiti sthalam. (homotopy pondikaina anubandha mariyu homotopy pondikaina commutative rendintinee vivarinche oka operaadnu e φ-operad antaaru.)
nirvachanam.
sthalavignaana pradaesaalaloo samaroopa samuuham yokka charyatho operadla (saadhaarana) amarikalo, oka operad "a" anedi "a" ≤-operad anie cheppabadutundi, daani khaaliilu "a" ("n") annee σ "n" ayithe-daani gunakaara charyatho vivikta khaaliilu σ "n" (samaroopa samuuham) kuu samaanamaina samaruupata. naan-cs operades (nonsimetric operades anie kooda pilustaaru, kramaparivartana laeni operades) amarikalo, oka operad "eah" anedi "eah" φ, daani anni khaaliilu "eah" ("enn") oppandaaniki vasthe. sthalavignaana pradaesaala kante itara vargalalo, "homotopy" mariyu "contractivity" yokka bhaavanalanu golusu samudaayaala vargamlooni homology samaanatvaalu vanti tagina analogues dwara bharti cheyali.
"a" "n" "-operades".
paribhaashalo "a" anae aksharam "anubandham" anie suuchistumdi, mariyu ananta chihnalu "anni" unnata homotopyla varaku anubandhata avasaramani chebutaayi. marinta saadhaaranamgaa, "a" "n"-operad ("n" ±n), oka nirdishta sthaayi homotopyla varaku matrame anubandhamgaa unde paramiti gunakaalu anae balaheenamaina bhavana undhi. mukhyamgaa,
"a" "φ-operades mariyu single loop space luu".
oka space "x" anedi maroka space yokka loop space, dheenini "bx" anie suuchistaaru, okavela mariyu "x" anedi oka suutram _ 1-operad meeda beejaganitam ayithe mariyu daani anusandhaaninchabadina bhagala yokka monoid "π" 0 ("x") oka samuuham ayithe matrame. oka suutram _ 1-operade paie unna beejaganitam suutram _ 3-space gaa suuchimchabadutumdi. loop spacela yokka eee lakshanaala yokka moodu parinaamaalu unnaayi. modata, loop space anedi oka suutram _ 1-space. rendavadi, anusandhaaninchabadina suutram _ 1-space "x" anedi loop space. moodavadi, bahusha disconnect cheyabadina formula _ 1-space yokka group completion anedi loop space.
homotopy siddhaantamlo formula _ 1-operades yokka praamukhyata formula _ 1-operades mariyu loop spacelapy algibras madhya eee sambandham nundi udbhavinchindi.
"a" "φ-alzebras".
suutram _ 1-operade paie unna beejaganitaanni suutram _ 1-beejaganitam antaaru. udaaharanalu symplectic manifold yokka fukaya varganni kaligi untaayi, dheenini nirvachinchagaliginappudu (sudoholomarphic vakrarekhanu kooda chudandi).
udaaharanalu.
atyanta spashtamaina, mukhyamgaa upayogakaramgaa lekapothe, suutram _ 1-operade yokka udaaharana suutram _ 12 dwara ivvabadina "associative operad" a ". eee operad khachitamgaa associative gunakaalanu vivaristundi. nirvachanam prakaram, edainaa itara suutram _ 1-operad "a" kuu myapnu kaligi untundi, idhi homotopy samaanatvam.
oka φ-operad yokka rekhaganita udaaharananu stasheff polytopes ledhaa associahedralu istayi.
takkuva mishrama udaaharana chinna viraamaala yokka operade space formula _ 14 loe unit viramamlo "n" vidadeeyabadina viraamaala yokka anni ponduparachabadinavi untaayi.

