Commutative Algebras which are Formal as Associative

Student: Tereshkin Denis

Educational Programme: Mathematics (Master)

Final Grade: 10

Year of Graduation: 2019

In this work we prove that A_{\infty}-quasiisiomorphic C_{\infty}-algebras are C_{\infty}-quasiisiomorphic. As a corollary, relation of being quasiisomorphic on commutative dg algebras can be obtained by restriction from category of associative algebras. As a particular application, one obtains that two nilpotent finite type spaces have weakly equivalent rationalizations if and only if their rational cochain algebras are quasiisomorphic.

Full text (added June 6, 2019)

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