Algebraic & Geometric Topology

Infinity structure of Poincaré duality spaces

Thomas Tradler and Mahmoud Zeinalian

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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.

Article information

Algebr. Geom. Topol., Volume 7, Number 1 (2007), 233-260.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57P10: Poincaré duality spaces
Secondary: 57P05: Local properties of generalized manifolds

Poincaré duality space local infinity structure


Tradler, Thomas; Zeinalian, Mahmoud. Infinity structure of Poincaré duality spaces. Algebr. Geom. Topol. 7 (2007), no. 1, 233--260. doi:10.2140/agt.2007.7.233.

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