Batalin-Vilkovisky algebra structures on Hochschild cohomology

Menichi, Luc

doi:10.24033/bsmf.2576

Cited by 38 publications

(39 citation statements)

References 16 publications

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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%

“…Note that in [33] we forgot to twist the right action by the sign . 1/ jcjjf j and so have also a sign problem.…”

Section: Batalin-vilkovisky Algebra Structures On Hochschild Cohomologymentioning

confidence: 99%

“…[33], to prove Conjecture 4, it suffices to show that the composite FTV B J is a morphism of graded algebras.…”

Section: Conjecture 4 Suppose That (3) Holds Then There Is An Isomomentioning

confidence: 99%

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Van den Bergh isomorphisms in string topology

Menichi¹

2010

J. Noncommut. Geom.

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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%

“…Note that in [33] we forgot to twist the right action by the sign . 1/ jcjjf j and so have also a sign problem.…”

Section: Batalin-vilkovisky Algebra Structures On Hochschild Cohomologymentioning

confidence: 99%

“…[33], to prove Conjecture 4, it suffices to show that the composite FTV B J is a morphism of graded algebras.…”

Section: Conjecture 4 Suppose That (3) Holds Then There Is An Isomomentioning

confidence: 99%

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Van den Bergh isomorphisms in string topology

Menichi¹

2010

J. Noncommut. Geom.

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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%

On the Hochschild homology of open Frobenius algebras

Abbaspour¹

2016

J. Noncommut. Geom.

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Abstract. We prove that the shifted Hochschild chain complex C * (A, A) [m] of a symmetric open Frobenius algebra A of degree m has a natural homotopy coBV-algebra structure. As a consequence HH * (A, A) [m] and HH * (A, A ∨ )[−m] are respectively coBV and BV algebras. The underlying coalgebra and algebra structure may not be resp. counital and unital. We also introduce a natural homotopy BV-algebra structure on C * ( is an open Frobenius algebras. If A is commutative, we also introduce a natural BV structure on the shifted relative Hochschild homology HH * (A)[m− 1]. We conjecture that the product of this BV structure is identical to the GoreskyHingston[GH09a] product on the cohomology of free loop spaces when A is a commutative cochain algebra model for M .

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