Open Access
2009 On the chain-level intersection pairing for $PL$ pseudomanifolds
Greg Friedman
Homology Homotopy Appl. 11(1): 261-314 (2009).


James McClure recently showed that the domain for the intersection pairing of $PL$ chains on a $PL$ manifold $M$ is a subcomplex of $C∗(M) ⊗ C∗(M)$ that is quasi-isomorphic to $C∗(M) ⊗ C∗(M)$ and, more generally, that the intersection pairing endows $C∗(M)$ with the structure of a partially-defined commutative $DGA$. We generalize this theorem to intersection pairings of $PL$ intersection chains on $PL$ stratified pseudomanifolds and demonstrate the existence of a partial restricted commutative $DGA$ structure. This structure is shown to generalize the iteration of the Goresky-MacPherson intersection product. As an application, we construct an explicit "roof" representation of the intersection homology pairing in the derived category of sheaves and verify that this sheaf theoretic pairing agrees with that arising from the geometric Goresky-MacPherson intersection pairing.


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Greg Friedman. "On the chain-level intersection pairing for $PL$ pseudomanifolds." Homology Homotopy Appl. 11 (1) 261 - 314, 2009.


Published: 2009
First available in Project Euclid: 1 September 2009

zbMATH: 1213.55004
MathSciNet: MR2529162

Primary: 55N33 , 55N45 , 57Q65
Secondary: 57N80

Keywords: differential graded algebra , general position , Intersection homology , intersection product , pseudomanifold

Rights: Copyright © 2009 International Press of Boston

Vol.11 • No. 1 • 2009
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