2009
DOI: 10.24033/bsmf.2576
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Batalin-Vilkovisky algebra structures on Hochschild cohomology

Abstract: Abstract. -Let M be any compact simply-connected oriented d-dimensional smooth manifold and let F be any field. We show that the Gerstenhaber algebra structure on the Hochschild cohomology on the singular cochains of M ,

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Cited by 39 publications
(39 citation statements)
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“…In this paper, we define a BatalinVilkovisky algebra structure on HH .S .G/; S .G// and an isomorphism of graded k-modules By [33], Proposition 28, c) follows directly from b). Note that when G is a discrete group, the algebra S .G/ of normalized singular chains on G is just the group ring kOEG.…”
Section: Conjecture 1 Let G Be a Topological Group Such That M Is A mentioning
confidence: 99%
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“…In this paper, we define a BatalinVilkovisky algebra structure on HH .S .G/; S .G// and an isomorphism of graded k-modules By [33], Proposition 28, c) follows directly from b). Note that when G is a discrete group, the algebra S .G/ of normalized singular chains on G is just the group ring kOEG.…”
Section: Conjecture 1 Let G Be a Topological Group Such That M Is A mentioning
confidence: 99%
“…This statement is the Eckmann-Hilton or Koszul dual of [33], Proposition 11. In this section we prove this statement if A is connected.…”
Section: The Isomorphism Between Hochschild Cohomology and Hochschildmentioning
confidence: 99%
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“…One approach is to use the Hochschild cohomology of closed Frobenius algebras [CJ02,Mer04,Tra08,TZ06,Kau07,Kau08,Men09,WW]. In particular Félix-Thomas [FT08] proved that over rationals and for any closed simply connected manifold M the Chas-Sullivan BV-algebra H * (LM ) is isomorphic to HH * (A) := HH * (A, A ∨ ) where A is a finite dimensional model (i.e.…”
Section: Introductionmentioning
confidence: 99%