Gorenstein spaces

Félix, Yves; Halperin, Stephen; Thomas, Jean‐Claude

doi:10.1016/0001-8708(88)90067-9

Cited by 86 publications

(113 citation statements)

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“…-A Batalin-Vilkovisky algebra is a Gerstenhaber algebra A equipped with a degree 1 linear map ∆ : A i → A i+1 such that ∆ • ∆ = 0 and such that the bracket is given by (9) {a, b} = (−1)…”

Section: Hochschild Homology and Cohomologymentioning

confidence: 99%

Batalin-Vilkovisky algebra structures on Hochschild cohomology

Menichi¹

2009

Bul. Soc. Math. France

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Section: Hochschild Homology and Cohomologymentioning

confidence: 99%

Batalin-Vilkovisky algebra structures on Hochschild cohomology

Menichi¹

2009

Bul. Soc. Math. France

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“…Moreover, it is natural with respect to (A, d). As a particular case, ev C * (X,K) is called the evaluation map of X over K On the other hand, the authors of [7] introduced the concept of a Gorenstein space over K. It is a space…”

Section: Evaluation Map and Gorenstein Spacesmentioning

confidence: 99%

A new lower bound for LS-category

Rami

2017

Arab. J. Math.

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Let X be a simply connected CW-complex of finite type and K an arbitrary field. In this paper, we use the Eilenberg-Moore spectral sequence of C * ( (X ), K) to introduce a new homotopical invariant r(X, K). If X is a Gorenstein space with nonzero evaluation map, then r(X, K) turns out to interpolate depth(H * ( (X ), K)) and e K (X ). We also define for any minimal Sullivan algebra ( V, d) a new spectral sequence and make use of it to associate to any 1-connected commutative differential graded algebraMathematics Subject Classification 55P62 · 55M30 · 55T20

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“…Proof See Félix-Halperin-Thomas [9,Chapter 14] for the CDGA case, and [7,Lemma A.3] for the special case of A D 0 in R-DGmod. The case for general A follows by standard techniques.…”

Section: Closed Model Category Factsmentioning

confidence: 99%

The rational homotopy type of a blow-up in the stable case

Lambrechts

Stanley

2008

Geom. Topol.

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Suppose f W V ! W is an embedding of closed oriented manifolds whose normal bundle has the structure of a complex vector bundle. It is well known in both complex and symplectic geometry that one can then construct a manifold W which is the blow-up of W along V . Assume that dim W 2 dim V C 3 and that H 1 .f / is injective. We construct an algebraic model of the rational homotopy type of the blow-up W from an algebraic model of the embedding and the Chern classes of the normal bundle. This implies that if the space W is simply connected then the rational homotopy type of W depends only on the rational homotopy class of f and on the Chern classes of the normal bundle.55P62, 14F35, 53C15, 53D05

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Gorenstein spaces

Cited by 86 publications

References 10 publications

Batalin-Vilkovisky algebra structures on Hochschild cohomology

Batalin-Vilkovisky algebra structures on Hochschild cohomology

A new lower bound for LS-category

The rational homotopy type of a blow-up in the stable case

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