String topology for spheres

Menichi, Luc

doi:10.4171/cmh/155

Cited by 32 publications

(55 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In characteristic non-zero, this does not hold in general, when using the homological Poincaré duality pairing, cf. Menichi [15] and Yang [24]. It is our hope, that the notion of ∞-inner products provides a suitable notion of chain level Poincaré duality to induce a model of the BV-algebra on the free loop space in the general setting.…”

Section: Annales De L'institut Fouriermentioning

confidence: 99%

“…, a n+1 , which are plugged into the Hochschild cochain. One calculates, that where, in the first two terms, we used the fact described in example 15 (15), that the strict unit can only multiply with one term, where it yields the identity. Similarly, we get the other terms as By definition 16 of the differential, we have that δ(ρ H ) = ρ δ(H) .…”

Section: Lemma 17 -∆ Is Cohomologous To the Operation Obtained By Thmentioning

confidence: 99%

See 1 more Smart Citation

The Batalin-Vilkovisky Algebra on Hochschild Cohomology Induced by Infinity Inner Products

Tradler¹

2008

Ann. inst. Fourier

126

View full text Add to dashboard Cite

We define a BV-structure on the Hochschild-cohomology of a unital, associative algebra A with a symmetric, invariant and non-degenerate inner product. The induced Gerstenhaber algebra is the one described in Gerstenhaber's original paper on Hochschild-cohomology. We also prove the corresponding theorem in the homotopy case, namely we define the BV-structure on the Hochschild-cohomology of a unital A∞-algebra with a symmetric and non-degenerate ∞-inner product.

show abstract

Section: Annales De L'institut Fouriermentioning

confidence: 99%

Section: Lemma 17 -∆ Is Cohomologous To the Operation Obtained By Thmentioning

confidence: 99%

The Batalin-Vilkovisky Algebra on Hochschild Cohomology Induced by Infinity Inner Products

Tradler¹

2008

Ann. inst. Fourier

126

View full text Add to dashboard Cite

show abstract

“…For instance Menichi [22] proved that algebras H * (LS are isomorphic as Gerstenhaber algebras but not as BV-algebras for Z/2-coefficients.…”

mentioning

confidence: 99%

Rational BV-algebra in string topology

Félix¹,

Thomas²

2008

Bul. Soc. Math. France

View full text Add to dashboard Cite

Abstract. -Let M be a 1-connected closed manifold of dimension m and LM be the space of free loops on M . M. Chas and D. Sullivan defined a structure of BValgebra on the singular homology of LM , H * (LM ; k). When the ring of coefficients is a field of characteristic zero, we prove that there exists a BV-algebra structure on the Hochschild cohomology HH * (C * (M ); C * (M )) which extends the canonical structure of Gerstenhaber algebra. We construct then an isomorphism of BV-algebras between HH * (C * (M ); C * (M )) and the shifted homology H * +m (LM ; k). We also prove that the Chas-Sullivan product and the BV-operator behave well with a Hodge decomposition of H * (LM ).Texte reçu le 7 juin

show abstract

“…On the other hand, combining the results from [52] and [5] one deduces that SH * (T * S 2 ) ∼ = HH * (C 2− * (ΩS 2 )) ∼ = HH * (C * (S 2 )) does not admit a dilation over a field of characteristic 2 4 . Recall that a dilation is an element b ∈ SH 1 (X Γ ) such that ∆b = 1 where ∆ : SH * (X Γ ) → SH * −1 (X Γ ) is the BV-operator in symplectic cohomology.…”

Section: Recall That a Derivation Is A Linear Mapmentioning

confidence: 90%

Koszul duality patterns in Floer theory

Etgü

Lekili

2017

Geom. Topol.

View full text Add to dashboard Cite

We study symplectic invariants of the open symplectic manifolds X Γ obtained by plumbing cotangent bundles of 2-spheres according to a plumbing tree Γ. For any tree Γ, we calculate (DG-)algebra models of the Fukaya category F(X Γ ) of closed exact Lagrangians in X Γ and the wrapped Fukaya category W(X Γ ). When Γ is a Dynkin tree of type A n or D n (and conjecturally also for E 6 , E 7 , E 8 ), we prove that these models for the Fukaya category F(X Γ ) and W(X Γ ) are related by (derived) Koszul duality. As an application, we give explicit computations of symplectic cohomology of X Γ for Γ = A n , D n , based on the Legendrian surgery formula of [14]. In the case that Γ is non-Dynkin, we obtain a spectral sequence that converges to symplectic cohomology whose E 2 -page is given by the Hochschild cohomology of the preprojective algebra associated to the corresponding Γ. It is conjectured that this spectral sequence is degenerate if the ground field has characteristic zero.

show abstract

String topology for spheres

Cited by 32 publications

References 21 publications

The Batalin-Vilkovisky Algebra on Hochschild Cohomology Induced by Infinity Inner Products

The Batalin-Vilkovisky Algebra on Hochschild Cohomology Induced by Infinity Inner Products

Rational BV-algebra in string topology

Koszul duality patterns in Floer theory

Contact Info

Product

Resources

About