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2007 Infinity structure of Poincaré duality spaces
Thomas Tradler, Mahmoud Zeinalian
Algebr. Geom. Topol. 7(1): 233-260 (2007). DOI: 10.2140/agt.2007.7.233

Abstract

We show that the complex CX of rational simplicial chains on a compact and triangulated Poincaré duality space X of dimension d is an A coalgebra with duality. This is the structure required for an A version of the cyclic Deligne conjecture. One corollary is that the shifted Hochschild cohomology HH+d(CX,CX) of the cochain algebra CX with values in CX has a BV structure. This implies, if X is moreover simply connected, that the shifted homology H+dLX of the free loop space admits a BV structure. An appendix by Dennis Sullivan gives a general local construction of structures.

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Thomas Tradler. Mahmoud Zeinalian. "Infinity structure of Poincaré duality spaces." Algebr. Geom. Topol. 7 (1) 233 - 260, 2007. https://doi.org/10.2140/agt.2007.7.233

Information

Received: 21 August 2005; Revised: 16 September 2006; Accepted: 22 January 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1137.57025
MathSciNet: MR2308943
Digital Object Identifier: 10.2140/agt.2007.7.233

Subjects:
Primary: 57P10
Secondary: 57P05

Rights: Copyright © 2007 Mathematical Sciences Publishers

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