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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
On the chain-level intersection pairing for PL manifolds

J E McClure

Geometry & Topology 10 (2006) 1391–1424

Erratum: Geometry & Topology 13 (2009) 1775–1777

arXiv: math.QA/0410450

Abstract

Let M be a compact oriented PL manifold and let CM be its PL chain complex. The domain of the chain-level intersection pairing is a subcomplex of CM CM. We prove that the inclusion map from this subcomplex to CM CM is a quasi-isomorphism. An analogous result is true for the domain of the iterated intersection pairing. Using this, we show that the intersection pairing gives CM a structure of partially defined commutative DGA, which in particular implies that CM is canonically quasi-isomorphic to an E chain algebra.

Keywords
intersection pairing, partial algebra, general position
Mathematical Subject Classification 2000
Primary: 18D50
Secondary: 57Q65
References
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Publication
Received: 22 October 2004
Accepted: 14 July 2005
Published: 4 October 2006
Proposed: Gunnar Carlsson
Seconded: Haynes Miller, Bill Dwyer
Authors
J E McClure
Department of Mathematics
Purdue University
150 N University Street
West Lafayette, IN 47907-2067
USA