Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 7, Number 1 (2007), 233-260.
Infinity structure of Poincaré duality spaces
We show that the complex of rational simplicial chains on a compact and triangulated Poincaré duality space of dimension is an 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 of the cochain algebra with values in has a BV structure. This implies, if is moreover simply connected, that the shifted homology of the free loop space admits a BV structure. An appendix by Dennis Sullivan gives a general local construction of structures.
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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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. https://projecteuclid.org/euclid.agt/1513796666