Preprints, books, papers

arXived:

  • Modular categories as representations of the 3-dimensional bordism 2-category

    (with B. Bartlett, C. Schommer-Pries, and J. Vicary)
    View abstract or pdf

  • Extended 3-dimensional bordism as the theory of modular objects

    (with B. Bartlett, C. Schommer-Pries, and J. Vicary)
    View abstract or pdf

  • Internal bicategories

    (with A. Henriques)
    View abstract or pdf

Books:

  • Dualizable tensor categories

    (with C. Schommer-Pries and N. Snyder)
    Mem. Amer. Math. Soc. (2017), to appear.
    View abstract or pdf

  • Fusion of Defects (a.k.a. Conformal nets III)

    (with A. Bartels and A. Henriques)
    Mem. Amer. Math. Soc. (2017), to appear.
    View abstract or pdf

  • Cornered Heegaard Floer Homology

    (with R. Lipshitz and C. Manolescu)
    Mem. Amer. Math. Soc. (2017), to appear.
    View abstract or pdf

  • Topological Modular Forms

    (with J.Francis, A. Henriques, and M. Hill)
    Math. Surveys and Monographs 201 (2014), 351 pp.
    Available in hardcover

Published:

  • The balanced tensor product of module categories

    (with C. Schommer-Pries and N. Snyder)
    Kyoto J. Math. (2017), to appear.
    View abstract or pdf

  • Conformal nets IV: the 3-category

    (with A. Bartels and A. Henriques)
    Algebr. Geom. Topol. (2017), to appear.
    View abstract or pdf

  • Conformal nets II: conformal blocks

    (with A. Bartels and A. Henriques)
    Comm. Math. Phys. 354 (2017), 393–458.
    View abstract or pdf

  • Conformal nets I: coordinate-free nets

    (with A. Bartels and A. Henriques)
    Int. Math. Res. Not. 13 (2015), 4975-5052.
    View abstract or pdf

  • Dualizability and index of subfactors

    (with A. Bartels and A. Henriques)
    Quantum Topology 5 (2014), 289-345.
    View abstract or pdf

  • On the algebra of cornered Floer homology

    (with C. Manolescu),
    J. Topology 7 (2014), 1-68. 
    View abstract or pdf

  • Fusion rings of loop group representations

    Comm. Math. Phys. 319 (2013), 395-423. 
    View abstract or pdf

  • Topological modular forms and conformal nets

    (with A. Henriques),
    In “Mathematical Foundations of QFT and Perturbative String Theory”,
    Proc. Sympos. Pure Math. 83 (2011), 341-354.
    View abstract or pdf

  • Homological obstructions to string orientations

    (with A. Henriques and M. Hill),
    Int. Math. Res. Not. 18 (2011), 4074-4088.
    View abstract or pdf

  • Higher topological cyclic homology and the Segal conjecture for tori

    (with G. Carlsson and B. Dundas),
    Adv. Math. 226 (2011), 1823-1874. 
    View abstract or pdf

  • On the structure of the fusion ideal

    Comm. Math. Phys. 290 (2009), 335-355. 
    View abstract or pdf

  • On the twisted K-homology of simple Lie groups

    Topology 45 (2006), 955-988. 
    View abstract or pdf

  • On the fibrewise Poincare-Hopf theorem

    In “Recent Developments in Algebraic Topology”,
    Contemp. Math. 407 (2006), 101-111.
    View pdf

  • Trace and transfer maps in the algebraic K-theory of spaces

    K-Theory 36 (2005), 59-82.
    View pdf

  • Twisted parametrized stable homotopy theory

    In “Twisted stable homotopy theory”,
    PhD Thesis, MIT 33095 (2005), 14-79.
    View abstract or pdf