S-Space College of Natural Sciences (자연과학대학) Dept. of Mathematical Sciences (수리과학부) Theses (Ph.D. / Sc.D._수리과학부)
Homotopy cyclic A-infinity algebras, potentials and related cohomology theories
호모토피 순환 A-무한대수, 잠재함수와 코호몰로지 이론
- 자연과학대학 수리과학부
- Issue Date
- 서울대학교 대학원
- 학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2013. 2. 조철현.
- An A-infinity algebra has "associative up to homotopy" structure. For an A-infinity algebra $A$, we give a definition of strong homotopy inner products(if exist) which is the homotopy notion of cyclic inner products due to Kontsevich. From strong homotopy inner products we get several invariants which we call "potentials". We study their homotopy natures, gauge invariances etc. Also we find an explicit correspondence between cohomology elements of $A$ and isomorphism classes of strong homotopy inner products on $A$.