Volume 7, issue 1 (2007)

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Infinity structure of Poincaré duality spaces

Thomas Tradler and Mahmoud Zeinalian

Appendix: Dennis Sullivan

Algebraic & Geometric Topology 7 (2007) 233–260

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.

Poincaré duality space, local infinity structure
Mathematical Subject Classification 2000
Primary: 57P10
Secondary: 57P05
Received: 21 August 2005
Revised: 16 September 2006
Accepted: 22 January 2007
Published: 29 March 2007
Thomas Tradler
Department of Mathematics
College of Technology of the City University of New York
300 Jay Street
Brooklyn NY 11201
Mahmoud Zeinalian
Department of Mathematics
C W Post Campus of Long Island University
720 Northern Boulevard
Brookville NY 11548
Dennis Sullivan
Department of Mathematics
Graduate Center of the City University of New York
365 Fifth Avenue
New York NY 10016