Tom MrowkaMathematics at MIT

Publications

Papers and books

A selected list emphasizing recent work and several major themes. A complete chronological bibliography appears in the full CV.

Complete CV and bibliographyarXiv author search

Preprints

Current work

  1. SU(3) instanton homology for webs and foams
    With P. B. Kronheimer. 2025.
    arXiv:2505.02755

Selected papers

Instantons, knots, and webs

  1. Relations in singular instanton homology
    With P. B. Kronheimer. Geometry & Topology 29 (2025), 1975-2046.
    arXivJournal / DOI
  2. Instantons and some concordance invariants of knots
    With P. B. Kronheimer. Journal of the London Mathematical Society 104 (2021), 541-571.
    arXiv
  3. Instantons and Bar-Natan homology
    With P. B. Kronheimer. Compositio Mathematica 157 (2021), 484-528.
    arXivJournal / DOI
  4. A deformation of instanton homology for webs
    With P. B. Kronheimer. Geometry & Topology 23 (2019), 1491-1547.
    arXivJournal / DOI
  5. Tait colorings, and an instanton homology for webs and foams
    With P. B. Kronheimer. Journal of the European Mathematical Society 21 (2019), 55-119.
    arXivJournal / DOI
  6. Khovanov homology is an unknot-detector
    With P. B. Kronheimer. Publications Mathématiques de l'IHÉS 113 (2011), 97-208.
    arXivJournal / DOI
  7. Knot homology groups from instantons
    With P. B. Kronheimer. Journal of Topology 4 (2011), 835-918.
    arXivJournal / DOI
  8. Knots, sutures, and excision
    With P. B. Kronheimer. Journal of Differential Geometry 84 (2010), 301-364.
    arXivJournal / DOI
  9. Instanton Floer homology and the Alexander polynomial
    With P. B. Kronheimer. Algebraic & Geometric Topology 10 (2010), 1715-1738.
    arXivJournal / DOI

Selected papers

Three- and four-manifolds

  1. Monopoles and lens space surgeries
    With P. B. Kronheimer, P. S. Ozsváth, and Z. Szabó. Annals of Mathematics 165 (2007), 457-546.
    arXivJournal / DOI
  2. Witten's conjecture and Property P
    With P. B. Kronheimer. Geometry & Topology 8 (2004), 295-310.
    arXivJournal / DOI
  3. Embedded surfaces and the structure of Donaldson's polynomial invariants
    With P. B. Kronheimer. Journal of Differential Geometry 41 (1995), 573-734.
    Journal / DOI
  4. Gauge theory for embedded surfaces I
    With P. B. Kronheimer. Topology 32 (1993), 773-826.
    Journal / DOI
  5. Irreducible 4-manifolds need not be complex
    With R. E. Gompf. Annals of Mathematics 138 (1993), 61-111.
    Journal / DOI

Books

Monographs

  1. Monopoles and Three-Manifolds
    With P. B. Kronheimer. Cambridge University Press, 2007.
    Publisher / DOI
  2. The L²-Moduli Space and a Vanishing Theorem for Donaldson Polynomial Invariants
    With J. W. Morgan and D. Ruberman. International Press, 1994.