Greg Friedman
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View article: Foundations of geometric cohomology: from co-orientations to product structures
Foundations of geometric cohomology: from co-orientations to product structures Open
This manuscript develops a geometric approach to ordinary cohomology of smooth manifolds, constructing a cochain complex model based on co-oriented smooth maps from manifolds with corners. Special attention is given to the pull-back produc…
View article: Chern classes and unitary equivalence of normal matrices over topological spaces
Chern classes and unitary equivalence of normal matrices over topological spaces Open
This paper continues the authors' work on the question of unitary equivalence of matrices with entries in the complex-valued functions of a topological space (matrices over spaces). Specifically, we here consider the question of unitary eq…
View article: Intersection homology duality and pairings: singular, PL and sheaf-theoretic
Intersection homology duality and pairings: singular, PL and sheaf-theoretic Open
We compare the sheaf-theoretic and singular chain versions of Poincare\nduality for intersection homology, showing that they are isomorphic via\nnaturally defined maps. Similarly, we demonstrate the existence of canonical\nisomorphisms bet…
View article: Flowing from intersection product to cup product
Flowing from intersection product to cup product Open
We use a vector field flow defined through a cubulation of a closed manifold to reconcile the partially defined commutative product on geometric cochains with the standard cup product on cubical cochains, which is fully defined and commuta…
View article: Generalizations of Intersection Homology and Perverse Sheaves with Duality over the Integers
Generalizations of Intersection Homology and Perverse Sheaves with Duality over the Integers Open
We provide a generalization of the Deligne sheaf construction of intersection homology theory, and a corresponding generalization of Poincaré duality on pseudomanifolds, such that the Goresky-MacPherson, Goresky-Siegel, and Cappell-Shaneso…
View article: Topological invariance of torsion sensitive intersection homology
Topological invariance of torsion sensitive intersection homology Open
Torsion sensitive intersection homology was introduced to unify several versions of Poincare duality for stratified spaces into a single theorem. This unified duality theorem holds with ground coefficients in an arbitrary PID and with no l…
View article: Two short proofs of the topological invariance of intersection homology
Two short proofs of the topological invariance of intersection homology Open
We indicate two short proofs of the Goresky-MacPherson topological invariance of intersection homology. One proof is very short but requires the Goresky-MacPherson support and cosupport axioms; the other is slightly longer but does not req…
View article: Generalizations of intersection homology with duality over the integers
Generalizations of intersection homology with duality over the integers Open
We provide a generalization of the Deligne sheaf construction of intersection homology theory and a corresponding generalization of Poincare duality on pseudomanifolds such that the Goresky-MacPherson, Goresky-Siegel, and Cappell-Shaneson …
View article: The chain-level intersection pairing for PL pseudomanifolds revisited
The chain-level intersection pairing for PL pseudomanifolds revisited Open
We generalize the PL intersection product for chains on PL manifolds and for intersection chains on PL stratified pseudomanifolds to products of locally finite chains on non-compact spaces that are natural with respect to restriction to op…