GREG FRIEDMAN

E-mail:g.friedman@tcu.edu

Department of Mathematics
Texas Christian University
TCU Box 298900
Fort Worth, TX 76129
Ph. 817-257-6343

• I'm co-organizing an NSF/CBMS Conference at TCU on Hodge Theory, Complex Geometry, and Representation Theory , June 18-22, 2012, with principal lecturer Phillip Griffiths.
• I'm co-organizing a special session on Geometric Topology and Geometric Group Theory at the 46th Spring Topology and Dynamics Conference, March 22-24, 2012, at the Universidad Nacional Autonoma de Mexico (UNAM)
• Here are some notes on doing proofs that I'm (in theory still) working on. They're intended for undergraduates just learning how to prove things. Eric Schecter at Vanderbilt has a related useful page on Common Errors in Undergraduate Mathematics
• Here's a handy guide I wrote for evaluating integrals in vector calculus:
• Here are some extremely brief notes on spectral sequences for a seminar talk.
• And here are some topology notes, written by others, that I've acquired over time. These are mostly hard-to-find seminar notes and the like.
• Slides for my talk on Poincaré Duality on Homotopically Stratified Spaces given at Singularities in Geometry and Topology, in honor of the 60th birthday of Sylvain Cappell, March 17, 2008. Here is a more printer friendly version of the same talk without overlays.
• I co-organized the NSF/CBMS Conference on Topology, C*-algebras, and String Duality, May 18-22, 2009, with principal lecturer Jonathan Rosenberg of the University of Maryland.
• I co-organized an MSRI Workshop on the Topology of Stratified Spaces in September, 2008.

Research Interests:

Publications

Submitted papers:

• Cup and cap products in intersection (co)homology (with James McClure, Purdue University)
  arxiv link (44 pages)
  
  
• The symmetric signature of a Witt space (with James McClure, Purdue University)
  arxiv link (31 pages)

Accepted publications:

• An elementary illustrated introduction to simplicial sets
  To appear in the Rocky Mountain Journal of Mathematics
  pdf (57 pages)
  
  
• Additivity and non-additivity for perverse signatures (with Eugénie Hunsicker, Loughborough University)
  To appear in Journal für die reine und angewandte Mathematik (Crelle's Journal)
  pdf (45 pages)
  
  
• 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, 177-222
  pdf (41 pages)
  
  
• 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), 103-135
  pdf (40 pages)
  
  
• On the chain-level intersection pairing for PL pseudomanifolds
  Homology, Homotopy and Applications 11 (2009), 261-314
  pdf (51 pages)
  
  
• Intersection homology and Poincaré duality on homotopically stratified spaces
  Geometry and Topology 13 (2009), 2163-2204
  pdf (36 pages)
  
  
• Intersection homology with field coefficients: K-Witt spaces and K-Witt bordism
  Communications on Pure and Applied Mathematics 62 (2009), 1265-1292
  pdf - ps (26 pages)
  
  
• Intersection homology Kunneth theorems
  Mathematische Annalen 343 (2009), 371-395
  pdf - ps (25 pages)
  
  
• Intersection homology of stratified fibrations and neighborhoods
  Advances in Mathematics 215 (2007), 24-65
  pdf - ps (45 pages)
  
  
• Cobordism of disk knots
  Israel Journal of Mathematics 163 (2008), 139-188 pdf ps (42 pages)
  
  
• There exist non-trivial PL knots whose complements are homotopy circles
  Fundamenta Mathematicae 193 (2007), 1-6
  pdf - ps (7 pages)
  
  
• 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, 205-224
  pdf - ps (18 pages)
  
  
• Singular chain intersection homology for traditional and super-perversities
  Transactions of the American Mathematical Society 359 (2007), 1977-2019
  pdf - ps (46 pages)
  
  
• Superperverse intersection cohomology: stratification (in)dependence
  Mathematische Zeitschrift 252 (2006), 49 - 70
  pdf - ps (21 pages)
  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)
  pdf - ps (23 pages)
  
  
• Triangulations of 3-dimensional pseudomanifolds with an application to state-sum invariants (with Markus Banagl, Universitat Heidelberg)
  Algebraic and Geometric Topology 4 (2004), 521-542
  pdf - ps (22 pages)
  
  
• Intersection homology of regular and cylindrical neighborhoods
  Topology and Its Applications 149 (2005), 97-148
  pdf - ps (49 pages)
  
  
• Groups of locally-flat disk knots and non-locally-flat sphere knots
  Journal of Knot Theory and Its Ramifications 14 (2005), 189-215
  pdf - ps (25 pages)
  
  
• All frame-spun knots are slice
  Proceedings of the American Mathematical Society 132 (2004), 3103-3109
  pdf - ps (8 pages)
  
  
• Stratified fibrations and the intersection homology of the regular neighborhoods of bottom strata
  Topology and Its Applications 134 (2003), 69-109
  pdf - ps
  
  
• Intersection Alexander polynomials
  Topology 43 (2004), 71-117
  pdf - ps
  
  
• Alexander polynomials of non-locally-flat knots
  Indiana University Mathematics Journal 52 (2003), 1479-1578
  pdf - ps