scholarly journals Rational BV-algebra in string topology

2008 ◽  
Vol 136 (2) ◽  
pp. 311-327 ◽  
Author(s):  
Yves Félix ◽  
Jean-Claude Thomas
Keyword(s):  
String Topology ◽  
Bv Algebra

scholarly journals Higher Brackets on Cyclic and Negative Cyclic (Co)Homology

2018 ◽  
Vol 2020 (23) ◽  
pp. 9148-9209
Author(s):  
Domenico Fiorenza ◽  
Niels Kowalzig
Keyword(s):  
Hochschild Cohomology ◽  
Cyclic Homology ◽  
Cyclic Cohomology ◽  
Algebra Structure ◽  
String Topology ◽  
Cohomology Groups ◽  
Poincare Duality ◽  
Homology Groups ◽  
Bv Algebra ◽  
Special Case

Abstract The purpose of this article is to embed the string topology bracket developed by Chas–Sullivan and Menichi on negative cyclic cohomology groups as well as the dual bracket found by de Thanhoffer de Völcsey–Van den Bergh on negative cyclic homology groups into the global picture of a noncommutative differential (or Cartan) calculus up to homotopy on the (co)cyclic bicomplex in general, in case a certain Poincaré duality is given. For negative cyclic cohomology, this in particular leads to a Batalin–Vilkoviskiĭ (BV) algebra structure on the underlying Hochschild cohomology. In the special case in which this BV bracket vanishes, one obtains an $e_3$-algebra structure on Hochschild cohomology. The results are given in the general and unifying setting of (opposite) cyclic modules over (cyclic) operads.

scholarly journals Hodge decomposition of string topology

2021 ◽  
Vol 9 ◽  
Author(s):  
Yuri Berest ◽  
Ajay C. Ramadoss ◽  
Yining Zhang
Keyword(s):  
Lie Algebras ◽  
General Theorem ◽  
Hodge Decomposition ◽  
String Topology ◽  
Free Loop Space ◽  
Oriented Manifold ◽  
Universal Enveloping Algebras ◽  
Finite Dimensional ◽  
Equivariant Homology ◽  
Simply Connected

Abstract Let X be a simply connected closed oriented manifold of rationally elliptic homotopy type. We prove that the string topology bracket on the $S^1$ -equivariant homology $ {\overline {\text {H}}}_\ast ^{S^1}({\mathcal {L}} X,{\mathbb {Q}}) $ of the free loop space of X preserves the Hodge decomposition of $ {\overline {\text {H}}}_\ast ^{S^1}({\mathcal {L}} X,{\mathbb {Q}}) $ , making it a bigraded Lie algebra. We deduce this result from a general theorem on derived Poisson structures on the universal enveloping algebras of homologically nilpotent finite-dimensional DG Lie algebras. Our theorem settles a conjecture of [7].

scholarly journals String topology for Lie groups

2010 ◽  
Vol 3 (2) ◽  
pp. 424-442 ◽  
Author(s):  
Richard A. Hepworth
Keyword(s):  
Lie Groups ◽  
String Topology

scholarly journals On string topology of classifying spaces

2015 ◽  
Vol 281 ◽  
pp. 394-507 ◽  
Author(s):  
Richard Hepworth ◽  
Anssi Lahtinen
Keyword(s):  
String Topology ◽  
Classifying Spaces
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