GREG FRIEDMAN
Department of Mathematics
Texas Christian University
TCU Box 298900
Fort Worth, TX 76129
Ph. 8172576343
Email:g.friedman@tcu.edu
Teaching information
Forthcoming for Fall 2021
Slides and notes
Research
My research interests are in algebraic and geometric topology, especially stratified spaces, intersection homology, and knot theory.
From 2013 to 2017 my work was supported by a grant from the National Science Foundation (DMS1308306). Some of my work was also supported by a grant from the Simons Foundation (#209127 to Greg Friedman, 20112014).
Vitae
My CV
My CV in TCU format
Publications
Preprints:
Accepted publications:

Two short proofs of the topological invariance of intersection homology
To appear in the
Proceedings of the 16th International Workshop on Real and Complex Singularities

My book Singular Intersection Homology
New Mathematical Monographs, vol. 33
Cambridge University Press, 2020
xiii+798 pages
preliminary manuscript format

Intersection homology duality and pairings: singular, PL, and sheaftheoretic (with James McClure, Purdue University)
To appear in Algebraic & Geometric Topology

Generalizations of intersection homology and perverse sheaves with duality over the integers (56
pages)
Michigan Mathematical Journal 68 (2019), 675726

The chainlevel intersection pairing for PL pseudomanifolds revisited
Journal of Singularities 17 (2018) 330367

Unitary equivalence of normal matrices over topological spaces (with Efton Park, TCU)
Journal of Topology and Analysis 8 (2016), 313348

Stratified and unstratified bordism of pseudomanifolds
Topology and Its Applications 194 (2015), 5192

Hodge theory, complex geometry, and representation theory
Robert S. Doran, Greg Friedman, and Scott Nollet (editors)
Contemporary Mathematics Volume 608, American Mathematical Society, 2014

The symmetric signature of a Witt space (with James McClure, Purdue University)
Journal of Topology and Analysis 5 (2013), 121159

Cup and cap products in intersection (co)homology (with James McClure, Purdue University)
Advances in Mathematics 240 (2013), 383426

KWitt bordism in characteristic 2
Archiv der Mathematik 100 (2013), 381387

Additivity and nonadditivity for perverse signatures (with Eugénie Hunsicker, Loughborough University)
Journal für die reine und angewandte Mathematik (Crelle's Journal) 676 (2013), 5195

An elementary illustrated introduction to simplicial sets
Rocky Mountain Journal of Mathematics 42 (2012), 353424
This version (which should coincide with the most uptodate version on the arxiv) contains errata to the published version.

Topology of Stratified Spaces
Greg Friedman, Eugénie Hunsicker, Anatoly Libgober, Laurentiu Maxim (editors)
Mathematical Sciences Research Institute Publications 58, Cambridge University Press 2011

An introduction to intersection homology with general perversity functions,
in Topology of Stratified Spaces ,
Greg Friedman, Eugénie Hunsicker, Anatoly Libgober, Laurentiu Maxim (editors)
Mathematical Sciences Research Institute Publications 58, Cambridge University Press 2011, 177222

Superstrings, Geometry, Topology, and C* Algebras
Robert S. Doran, Greg Friedman, Jonathan Rosenberg (editors)
Proceedings of Symposia in Pure Mathematics 81, Providence: American Mathematical Society, 2010

Intersection homology with general perversities
Geometria Dedicata 148 (2010), 103135

On the chainlevel intersection pairing for PL pseudomanifolds
Homology, Homotopy and Applications 11 (2009), 261314

Intersection homology and Poincaré duality on homotopically stratified spaces
Geometry and Topology 13 (2009), 21632204

Intersection homology with field coefficients: KWitt spaces and KWitt bordism
Communications on Pure and Applied Mathematics 62 (2009), 12651292
Please also see the Corrigendum, which addresses an error in characteristic 2.
The Corrigendum was printed in Communications on Pure and Applied Mathematics 65 (2012), 1639–1640

Intersection homology Kunneth theorems
Mathematische Annalen 343 (2009), 371395

Intersection homology of stratified fibrations and neighborhoods
Advances in Mathematics 215 (2007), 2465

Cobordism of disk knots
Israel Journal of Mathematics 163 (2008), 139188

There exist nontrivial PL knots whose complements are homotopy circles
Fundamenta Mathematicae 193 (2007), 16

A multiperversity generalization of intersection homology(with Gil Kalai, Hebrew University and Yale University)
Pure and Applied Mathematics Quarterly 3 (2007), Special Issue: In honor of Robert MacPherson, Part 3 of 3, 205224

Singular chain intersection homology for traditional and
superperversities
Transactions of the American Mathematical Society 359 (2007), 19772019

Superperverse intersection cohomology: stratification
(in)dependence
Mathematische Zeitschrift 252 (2006), 49  70
Important note: The citation to Glen Bredon's Topology and
Geometry is incorrect. Instead the citation should be to
Bredon's Sheaf Theory, 2nd Ed., Springer (1997).

Knot spinning
in the Handbook
of Knot Theory, edited by William Menasco and
Morwen Thistlethwaite, Elsevier Science (July 9, 2005)

Triangulations of 3dimensional pseudomanifolds with an application
to statesum invariants (with Markus Banagl, Universitat
Heidelberg)
Algebraic and Geometric Topology 4 (2004), 521542

Intersection homology of regular and cylindrical neighborhoods
Topology and Its Applications 149 (2005), 97148

Groups of locallyflat disk knots and nonlocallyflat sphere
knots
Journal of Knot Theory and Its
Ramifications 14 (2005), 189215

All framespun knots are slice
Proceedings of the American Mathematical Society 132 (2004),
31033109

Stratified fibrations and the intersection homology
of the regular neighborhoods of bottom strata
Topology and Its Applications 134 (2003), 69109

Intersection Alexander polynomials
Topology 43 (2004), 71117

Alexander polynomials of nonlocallyflat knots
Indiana
University Mathematics Journal 52 (2003), 14791578
Conferences
Here are some links to web sites for some of the conferences I've organized.
 Here is the archive web site for the Geometric Topology Workshops.
MPS Conference on Singularities: Geometric, Topological, and Analytic Aspects
 In August 2019 I was an organizer for Simons Foundation Conference on Singularities: Geometric, Topological, and Analytic Aspects in honor of Sylvain Cappell's 70th birthday.
 In February 2019, I was a coorganizer for Texas Geometry and Topology Conference.
 In June 2018, I coorganized an NSF/CBMS Regional Conference in the Mathematical Sciences on
Applications of Polynomial Systems with principal lecturer David A. Cox.
 In February, 2016, I was a coorganizer for Texas Geometry and Topology Conference.
 In June, 2015, I organized the 32nd annual Workshop in Geometric Topology.
 I coorganized an NSF/CBMS Conference at TCU on Hodge Theory, Complex Geometry, and Representation Theory , June 1822, 2012,
with principal lecturer Phillip Griffiths.
 I coorganized the NSF/CBMS Conference on Topology, C*algebras, and String Duality, May 1822, 2009,
with principal lecturer Jonathan Rosenberg of the University of Maryland.
 I coorganized an MSRI Workshop on the Topology of Stratified Spaces in September, 2008.