Mathematical Publications: Mark Goresky

1976

  • Geometric cohomology and homology of stratified objects (thesis)
    pdf file

    1977

  • La dualité de Poincaré pour les espaces singuliers (with R.MacPherson), C.R. Acad. Sci. Paris, Sér. A 284 (1977), 1549-1551

    1978

  • Triangulation of stratified objects. Proc. Amer. Math. Soc. 72 (1978), 193-200,
    pdf file (566K)

    1980

  • Intersection homology theory (with R. MacPherson) Topology 19 (1980), 135-162.
    pdf file (1.7 MB)


  • L2 cohomology and intersection homology of singular algebraic varieties (with J. Cheeger and R. MacPherson) in Differential Geometry Princeton University Annals of Math studies, S.T. Yau ed. Sept. 1981.
    Also translated into Russian and published by MIR Press, Moscow USSR.
    pdf file (2.2 MB)

    1981

  • Whitney stratified chains and cochains. Trans. Amer. Math. Soc. 267 (1981), 175-196.
    pdf file (2.1MB)


  • On the topology of complex algebraic maps (with R. MacPherson), Proc. of Conference on Algebraic Geometry in La Rabida, Spain. Springer Lecture Notes in Mathematics vol. 961 Springer Verlag, N.Y.
    pdf file (330K)

    1982

  • Stratified Morse theory (with R. MacPherson) Proc. of Symp. in Pure Math. 40 (1983), 517-533

  • Linking pairings on singular spaces (with P. Siegel) Comment. Math. Helv. 59 (1983), 96-110.
    pdf file (1.0 MB)


  • Morse theory for the intersection homology groups (with R.MacPherson) Analyse et Topologie sur les Espaces Singulieres, Astérisque 101 (1983), 135-192, Société Mathématique de France.
    pdf file (low res) (2.5 MB)
    pdf file (high res) (14 MB)

    1983

  • A decomposition theorem for the integral homology of a variety (with J. Carrell) Inv. Math. 73 (1983), 367-381.
    pdf file (1.5 MB)


  • Intersection homology II (with R. MacPherson), pdf file (4.7 MB), Inv. Math. 71 (1983), 77-129

  • Kazhdan-Lusztig polynomials for classical groups. (computer tables) Northeastern University preprint.

    1984

  • Four contributions to Seminar on Intersection Homology (A. Borel, ed.):
    1. Witt space cobordism
    2. Lefschetz fixed point theorem (with R. MacPherson)
    3. Sample computation of intersection homology (with R. MacPherson)
    4. Open problems and bibliography for intersection homology (with R. MacPherson)
    Progress in Mathematics vol 50, Birkhauser Boston, 1984.

  • Intersection homology operations. Comment. Math. Helv. 59 (1984), 485-505.
    pdf file (1.6 MB)

    1985

  • Lefschetz fixed point formula for intersection homology (with R. MacPherson). Comment. Math. Helv. 60 (1985), 366-391.
    pdf file (1.9 MB)

    1986

  • Simplicial intersection homology (with R. MacPherson). Appendix to ``Elementary construction of Perverse Sheaves'' by R. MacPherson and K.Vilonen. Inv. Math. 84 (1986), 432-433

  • Combinatorial geometries, Schubert varieties, and convex polyhedra (with I. M. Gelfand, R. MacPherson, and V. Serganova), Adv. Math. 63 (1987), 301-316.
    pdf file (730K)

    1987

  • On the topology of algebraic torus actions (with R. MacPherson), in Algebraic Groups: Utrecht 1986, Springer Lecture Notes in Mathematics vol 1271 (1987), 73-90.
    pdf file (660K)

    1988

  • Geometry of quadrics and their degenerations (with C. DeConcini, R. MacPherson, and C. Procesi), Comment. Math. Helv. 63 (1988), 337-413.
    pdf file (5.7 MB)

    1989

  • Stratified Morse Theory (with R. MacPherson). Springer Verlag, N. Y. (1989), Ergebnisse vol. 14.  

    (3 MB)  (get djvu viewer here)
    Also translated into Russian and published by MIR Press, Moscow, 1991.

  • Wu numbers of singular spaces (with W. Pardon), Topology 28 (1989), 325-367.
    pdf file (2.8 MB)

    1991

  • Piecewise linear differential forms with poles (with J. P. Brasselet and R. MacPherson), American Journal of Mathematics 113 (1991), 1019-1052.
    pdf file (1.7MB)

    1992

  • On the Kunneth formula for intersection cohomology (with Daniel Cohen and Lizhen Ji), Trans. Amer. Math. Soc. 333 (1992), 63-69.

  • L2 cohomology is intersection cohomology. in The Zeta Function of Picard Modular Surfaces,
    R. Langlands and D. Ramakrishnan, ed., Centre de Recherches Mathematiques, Univ. of Montreal Press, 1992, 47-64.
    pdf file (137KB)


  • Lefschetz numbers of Hecke correspondences (with R. MacPherson), in The Zeta Function of Picard Modular Surfaces,
    R. Langlands and D. Ramakrishnan, ed. Publ. C.R.M., Univ. of Montreal Press, 1992, 465-478.

    1993

  • The Local contribution to the Lefschetz Fixed Point Formula (with R. MacPherson), Inv. Math. 111 (1993), 1-33.
    pdf file (2.8 MB)

    1994

  • Weighted cohomology (with R. MacPherson and G. Harder), Inv. Math. 116 (1994), 139-213. pdf file (6.1 MB)

    1997

  • Discrete series characters and the Lefschetz formula for Hecke operators (with R. Kottwitz and R. MacPherson), Duke Math Journal 89 (1997), 477-554
    pdf file (6.0 MB)

    1998

  • Equivariant cohomology, Koszul duality, and the localization theorem (with R. Kottwitz and R. MacPherson), Inv. Math. 131 (1998), 25-83.
    pdf file (601 KB)

  • Toroidal and reductive Borel-Serre compactifications of locally symmetric spaces (with Y.-S. Tai), Amer. J. Math. 121 (1998), pp. 1095-1151.
    pdf file (452 KB)

    2000

  • L'algebre de cohomologie du complement, dans un espace affine (with P. Deligne and R. MacPherson) Mich. Math. J. 48 (2000), 121-136.
    pdf file (112 KB)

    2002

  • Chern classes of automorphic vector bundles (with W. Pardon), Invent. Math. 147 (2002), 561-612.
    pdf file (516KB)

  • Local intersection cohomology of the Baily-Borel compactification (with G. Harder, R. MacPherson, and A. Nair), Compositio Mathematica 134 (2002), 243-268.
    pdf file (280K)

    2003

  • The topological trace formula (with R. MacPherson), Crelle's J. 560 (2003), 77-150.
    pdf file (628K)

  • The moduli space of real abelian varieties with level structure (with Y.S. Tai) , Comp. Math. 139 (2003), 1-27.
    pdf file (312K)

  • Anti holomorphic multiplication and a real algebraic modular variety (with Y.S. Tai), J. Diff. Geom. 65 (2003), 513-560.
    pdf file (309K)

    2004

  • Homology of affine Springer fibers in the unramified case (with R. Kottwitz and R. MacPherson), Duke Math. J. 121 (2004), 509-561.
    pdf file (430K)

    2005

  • Regular points in affine Springer fibers (with R. Kottwitz and R. MacPherson), Michigan Math J. 53 (2005), 97-107.
    pdf file (170K)

  • Compactifications of modular varieties, in
    Harmonic Analysis, The Trace Formula, and Shimura Varieties,
    Proceedings of the Clay Mathematics Institute 2003 Summer School, Fields Institute, Toronto.
    J. Arthur, D. Ellwood, and R. Kottwitz, ed., Amer. Math. Soc. and Clay Math. Inst., 2005, pp. 551-582.
    pdf file (360K)

    2006

  • Purity of equivalued affine Springer fibers (with R. Kottwitz and R. MacPherson), Representation Theory, 10 (2006), 130-146.
    pdf file (421K)

    2009

  • Codimension of root valuation strata (with R. Kottwitz and R. MacPherson), Pure and Applied Mathematics Quarterly 5 (2009), 1253-1310.
    pdf file (380K)

  • Loop products and closed geodesics (with N. Hingston), Duke Math J. 150 (2009), 117-210.
    pdf file (770K)

    2010

  • On the spectrum of the equivariant cohomology ring (with R. MacPherson), Canad. J. Math. 62 (2010), 262-283.
    pdf file (200K)

    2012

  • Hilbert modular forms with coefficients in intersection homology (with Jayce Getz), Birkhauser, 2012

  • Algebraic Shift Register Sequences (with A. Klapper), Cambridge Univ. Press 2012

          

  • Introduction to the papers of R. Thom and J. Mather, Bull. Amer. Math. Soc. 49 (2012), 469-474. pdf file (360K)

     

    2015

  • Euler flag enumeration of Whitney stratified spaces (with R. Ehrenborg and M. Readdy)
       Advances in Mathematics 268 (2015), 85--128   pdf file

     

    2018

  • Commentary on "Numbers of Solutions of Equations in Finite Fields" by André Weil
      Bulletin of the AMS 55(3) (2018), 327--329  

     

    2019

  • Ordinary points mod p of GL(n,R) locally symmetric spaces (with Y. S. Tai), Pacific Journal of Mathematics 303(1) (2019), 165-215.
    pdf file

  • Real structures on Dieudonné modules (with Y. S. Tai), Pacific Journal of Mathematics 303(1) (2019), 217-241.
    pdf file

  • Armand Borel, 1923-2003, National Academy of Sciences, online collection of biographical memoirs, 2019.
    pdf file

     

    2020

  • Pfaffian integrals and invariants of singular varieties (with Paolo Aluffi), in A Panorma of Singularities, F.J.-C. Jiménez, ed.
        Contemporary Mathematics 742 (2020), 1-12. Amer. Math. Soc., Providence R.I., 2020.
    pdf file

  • Morse theory, stratifications and sheaves. in: Handbook of Geometry and Topology of Singularities
         (José Luis Cisneros-Molina, Lê Dung Tráng, José Seade ed.), Springer Verlag, N.Y., 2020, pp. 261-320.
    pdf file

     

    2022

  • Topological aspects of Boolean functions (with A. Björner and R. MacPherson)
        To appear in Pure and Applied Mathematics Quarterly
    Arxiv version

  • John Mather's contributions to singularity theory (To appear in Nat. Acad. Sci. Biographical Memoirs)
    pdf file

    2023

  • Morse theory for discrete magnetic operators and nodal count distribution for graphs (with L. Alon), J. Spectral Theory 13 (4) (2023), 1225-1260.
    Arxiv version