Mathematics – Quantum Algebra
Scientific paper
2004-10-20
Geom. Topol. 10 (2006) 1391-1424 and Geom. Topol. 13 (2009) 1775-1777
Mathematics
Quantum Algebra
This is the version published by Geometry & Topology on 4 October 2006 and includes the erratum published 12 March 2009
Scientific paper
10.2140/gt.2006.10.1391 10.2140/
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 G of C_*M\otimes C_*M. We prove that G is a "full" subcomplex, that is, the inclusion of G in C_*M \otimes 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_\infty chain algebra. An erratum is attached which corrects sign errors pointed out by Greg Friedman.
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