Books, preprints, papers
Books:
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Framed combinatorial topology
(with C. Dorn)
Math. Surveys and Monographs, to appear (2025), 309 pp.
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Fusion 2-categories and a state-sum invariant for 4-manifolds
(with D. Reutter)
Mem. Amer. Math. Soc., to appear (2024), 110 pp.
View abstract or pdf -
Dualizable tensor categories
(with C. Schommer-Pries and N. Snyder)
Mem. Amer. Math. Soc. 1308 (2021), 96 pp.
View abstract or pdf -
Cornered Heegaard Floer Homology
(with R. Lipshitz and C. Manolescu)
Mem. Amer. Math. Soc. 1266 (2019), 118 pp.
View abstract or pdf -
Fusion of Defects (a.k.a. Conformal nets III)
(with A. Bartels and A. Henriques)
Mem. Amer. Math. Soc. 1237 (2019), 108 pp.
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
arXived:
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Manifold diagrams and tame tangles
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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
Published:
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Conformal nets V: dualizability
(with A. Bartels and A. Henriques)
Comm. Math. Phys. 391. (2022), 1-31.
View abstract or pdf -
The balanced tensor product of module categories
(with C. Schommer-Pries and N. Snyder)
Kyoto J. Math. 59 (2019), 167-179.
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Conformal nets IV: the 3-category
(with A. Bartels and A. Henriques)
Algebr. Geom. Topol. 18 (2018), 897–956.
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Conformal nets II: conformal blocks
(with A. Bartels and A. Henriques)
Comm. Math. Phys. 354 (2017), 393–458.
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Conformal nets I: coordinate-free nets
(with A. Bartels and A. Henriques)
Int. Math. Res. Not. 13 (2015), 4975-5052.
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Dualizability and index of subfactors
(with A. Bartels and A. Henriques)
Quantum Topology 5 (2014), 289-345.
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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
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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
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Higher topological cyclic homology and the Segal conjecture for tori
(with G. Carlsson and B. Dundas),
Adv. Math. 226 (2011), 1823-1874.
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On the structure of the fusion ideal
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On the twisted K-homology of simple Lie groups
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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.
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Twisted parametrized stable homotopy theory
In “Twisted stable homotopy theory”,
PhD Thesis, MIT 33095 (2005), 14-79.
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