Geometry & Topology 10 (2006) 1391–1424

DOI: 10.2140/gt.2006.10.1391

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

arXiv: math.QA/0410450

Abstract

Let M be a compact oriented PL manifold and let C_*M be its PL chain complex. The domain of the chain-level intersection pairing is a subcomplex of C_*M⊗ C_*M. We prove that the inclusion map from this subcomplex to C_*M ⊗ C_*M 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 C_*M a structure of partially defined commutative DGA, which in particular implies that C_*M is canonically quasi-isomorphic to an E_∞ chain algebra.

Keywords

intersection pairing, partial algebra, general position

Mathematical Subject Classification

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