Cyclic homology and algebraic K-theory of spaces—II

Burghelea, Dan; Fiedorowicz, Zbigniew

doi:10.1016/0040-9383(86)90046-7

Cited by 99 publications

(77 citation statements)

References 12 publications

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“…As we know from results of Burghelea-Fiederowicz [10] and Goodwillie [31] that the Hochschild cohomology HH * (k [G]; k[G] ∨ ) is isomorphic as k-modules to H * (LBG; k). Therefore, we obtain Inspirational Theorem.…”

Section: Plan Of the Paper And Resultsmentioning

confidence: 99%

“…In [10,31], Burghelea, Fiedorowicz and Goodwillie proved that there is an isomorphism of vector spaces between H * (LBG) and HH * (S * (G); S * (G)). More precisely, they give a S 1 -equivariant weak homotopy equivalence γ : |ΓG| → LBG [43, 7.3.15].…”

Section: Lemma 55 the Morphism Of Left H * (G)-modulesmentioning

confidence: 99%

“…i)The composite of the isomorphism due to Burghelea, Fiedorowicz and Goodwillie [10,31] is a morphism of graded algebras between the algebra given by Corollary 36 and the underlying algebra on the Gerstenhaber algebra HH * (S * (G); S * (G)). ii)The isomorphism due to Burghelea, Fiedorowicz and Goodwillie [10,31] H * S 1 (LBG) ∼ = → HC * (S * (G)) 11.2.…”

Section: Lemma 55 the Morphism Of Left H * (G)-modulesmentioning

confidence: 99%

“…ii)The isomorphism due to Burghelea, Fiedorowicz and Goodwillie [10,31] H * S 1 (LBG) ∼ = → HC * (S * (G)) 11.2. The prop H −dχ(F ) (map * (F p+q /∂ in F, X)).…”

Section: Lemma 55 the Morphism Of Left H * (G)-modulesmentioning

confidence: 99%

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String topology of classifying spaces

Chataur

Menichi

2012

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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Abstract. Let G be a finite group or a compact connected Lie group and let BG be its classifying space. Let LBG := map(S 1 , BG) be the free loop space of BG i.e. the space of continuous maps from the circle S 1 to BG. The purpose of this paper is to study the singular homology H * (LBG) of this loop space. We prove that when taken with coefficients in a field the homology of LBG is a homological conformal field theory. As a byproduct of our main theorem, we get a Batalin-Vilkovisky algebra structure on the cohomology H * (LBG). We also prove an algebraic version of this result by showing that the Hochschild cohomology HH

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Section: Plan Of the Paper And Resultsmentioning

confidence: 99%

Section: Lemma 55 the Morphism Of Left H * (G)-modulesmentioning

confidence: 99%

Section: Lemma 55 the Morphism Of Left H * (G)-modulesmentioning

confidence: 99%

“…ii)The isomorphism due to Burghelea, Fiedorowicz and Goodwillie [10,31] H * S 1 (LBG) ∼ = → HC * (S * (G)) 11.2. The prop H −dχ(F ) (map * (F p+q /∂ in F, X)).…”

Section: Lemma 55 the Morphism Of Left H * (G)-modulesmentioning

confidence: 99%

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String topology of classifying spaces

Chataur

Menichi

2012

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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“…Here s denotes s W M ,! LM the inclusion of the constant loops into LM and BFG is the isomorphism of graded k-modules between the free loop space homology of M and the Hochschild homology of S .G/ introduced by Burghelea, Fiedorowicz [5] and Goodwillie [19]. Finally B denotes Connes' boundary on HH .S .G/; S .G//.…”

Section: Is a Quasiisomorphism If And Only If The Morphism Of Rightmentioning

confidence: 99%