On the chain-level intersection pairing for PL manifolds.
J.E. McClure
mcclure@math.purdue.edu
AMS classification numbers: 57Q65; 18D50
Posted on 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 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.
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