Proof of Swiss Cheese Version of Deligne's Conjecture

Details Proof of Swiss Cheese Version of Deligne's Conjecture Proof of Swiss Cheese Version of Deligne's Conjecture

2009-04-17

arxiv.org/abs/0904.2753v3

Mathematics

K-Theory and Homology

The article was rewritten. Multiple suggestions of referees were addressed. The paper is accepted for publication to IMRN

Scientific paper

10.1093/imrn/rnq265

For an associative algebra A we consider the pair "the Hochschild cochain complex C*(A,A) and the algebra A". There is a natural 2-colored operad which acts on this pair. We show that this operad is quasi-isomorphic to the singular chain operad of Voronov's Swiss Cheese operad. This statement is the Swiss Cheese version of the Deligne conjecture formulated by M. Kontsevich in arXiv:math/9904055.

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