On the chain-level intersection pairing for PL manifolds
摘要
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.
引用
@article{arxiv.math/0410450,
title = {On the chain-level intersection pairing for PL manifolds},
author = {J. E. McClure},
journal= {arXiv preprint arXiv:math/0410450},
year = {2014}
}
备注
This is the version published by Geometry & Topology on 4 October 2006 and includes the erratum published 12 March 2009