42 citations · 69 across the 29 of their papers we have counts for
33 papers
Bar cohomology of links: beyond Milnor invariants
Greg Friedman, Nir Gadish, Robin Koytcheff +2
We develop bar cohomology of link complements as an invariant of links in homology spheres. In this setting, bar cohomology is a Hopf algebra which is calculable using surfaces and…
The transverse singular complex
Greg Friedman, Anibal M. Medina-Mardones, Dev Sinha
Let be a smooth manifold without boundary and let be a countable collection of manifolds with corners, each equipped with a smooth map to . We show that the si…
Foundations of geometric cohomology: from co-orientations to product structures
Greg Friedman, Anibal M. Medina-Mardones, Dev Sinha
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…
Chern classes and unitary equivalence of normal matrices over topological spaces
Greg Friedman, Efton Park
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)…
Flowing from intersection product to cup product
Greg Friedman, Anibal M. Medina-Mardones, Dev Sinha
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 prod…
Topological invariance of torsion sensitive intersection homology
Greg Friedman
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…
Two short proofs of the topological invariance of intersection homology
Greg Friedman
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 cosu…
Intersection homology duality and pairings: singular, PL, and sheaf-theoretic
Greg Friedman, James E. McClure
We compare the sheaf-theoretic and singular chain versions of Poincare duality for intersection homology, showing that they are isomorphic via naturally defined maps. Similarly, we…
Generalizations of intersection homology and perverse sheaves with duality over the integers
Greg Friedman
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 chain-level intersection pairing for PL pseudomanifolds revisited
Greg Friedman
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-compac…
Stratified and unstratified bordism of pseudomanifolds
Greg Friedman
We study bordism groups and bordism homology theories based on pseudomanifolds and stratified pseudomanifolds. The main seam of the paper demonstrates that when we uses classes of…
Corrigendum to "Intersection homology with field coefficients: K-Witt spaces and K-Witt bordism"
Greg Friedman
This note corrects an error in the char(K)=2 case of the author's computation of the bordism groups of K-Witt spaces for the field K.
K-Witt bordism in characteristic 2
Greg Friedman
This note provides a computation of the bordism groups of K-Witt spaces for fields K with characteristic 2. We provide a complete computation for the unoriented bordism groups. For…
Cup and cap products in intersection (co)homology
Greg Friedman, James McClure
We construct cup and cap products in intersection (co)homology with field coefficients. The existence of the cap product allows us to give a new proof of Poincare duality in inters…
The symmetric signature of a Witt space
Greg Friedman, James McClure
Witt spaces are pseudomanifolds for which the middle-perversity intersection homology with rational coefficients is self-dual. We give a new construction of the symmetric signature…
Additivity and non-additivity for perverse signatures
Greg Friedman, Eugenie Hunsicker
A well-known property of the signature of closed oriented 4n-dimensional manifolds is Novikov additivity, which states that if a manifold is split into two manifolds with boundary…
An elementary illustrated introduction to simplicial sets
Greg Friedman
This is an expository introduction to simplicial sets and simplicial homotopy theory with particular focus on relating the combinatorial aspects of the theory to their geometric/to…
Intersection homology Kunneth theorems
Greg Friedman
Cohen, Goresky and Ji showed that there is a Kunneth theorem relating the intersection homology groups to and , prov…
On the chain-level intersection pairing for PL pseudomanifolds
Greg Friedman
James McClure recently showed that the domain for the intersection pairing of PL chains on a PL manifold is a subcomplex of that is quasi-isomorphic to $…
Intersection homology with field coefficients: -Witt spaces and -Witt bordism
Greg Friedman
We construct geometric examples of pseudomanifolds that satisfy the Witt condition for intersection homology Poincare duality with respect to certain fields but not others. We also…
Intersection homology and Poincaré duality on homotopically stratified spaces
Greg Friedman
We show that intersection homology extends Poincare duality to manifold homotopically stratified spaces (satisfying mild restrictions). This includes showing that, on such spaces,…
Intersection homology of stratified fibrations and neighborhoods
Greg Friedman
We derive spectral sequences for the intersection homology of stratified fibrations and approximate tubular neighborhoods in manifold stratified spaces. These neighborhoods include…
Knot spinning
Greg Friedman
This is an introduction to the construction of higher-dimensional knots by spinning methods. Simple spinning of classical knots was introduced by E. Artin in 1926, and several gene…
Triangulations of 3-dimensional pseudomanifolds with an application to state-sum invariants
Markus Banagl, Greg Friedman
We demonstrate the triangulability of compact 3-dimensional topological pseudomanifolds and study the properties of such triangulations, including the Hauptvermutung and relations…