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We implement an extended version of reflection positivity (Wick-rotated unitarity) for invertible topological quantum field theories and compute the abelian group of deformation classes using stable homotopy theory.
1905
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by same author, Consistency of M-theory on unorientable manifolds , arXiv:1908.09916
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by same author, A calculation of Pin + {\rm Pin}^{+} bordism groups , Comment. Math. Helv. 65
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Xianzhe Dai and Daniel S. Freed, η \eta -invariants and determinant lines , C. R. Acad. Sci. Paris Sér. I Math. 320
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J. P. C. Greenlees and J. P. May, Equivariant stable homotopy theory , Handbook of algebraic topology, North-Holland, Amsterdam, 1995, pp. 277–323
1995
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Alexander Altland and Martin R. Zirnbauer, Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures , Phys. Rev. B 55
1997
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by same author, Felix Klein Lectures 2011 . http://www.mpim-bonn.mpg.de/node/3372/abstracts
2011
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2011
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2011
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2012
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Scott Morrison and Kevin Walker, Blob homology , Geom. Topol. 16
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David Kazhdan, Introduction to QFT , Quantum fields and strings: a course for mathematicians. Vol. 1, pp. 377–418, American Mathematical Society, Providence, RI, 1999. Material from the Special Year on Quantum Field Theory held at the Institute for Advanced Study, Princeton, NJ, 1996–1997
1997
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Pierre Deligne, Notes on spinors , Quantum Fields and Strings: a course for mathematicians, Vol. 1, 2 (Princeton, NJ, 1996/1997), Amer. Math. Soc., Providence, RI, 1999, pp. 99–135
1999
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Pierre Deligne and John W. Morgan, Notes on supersymmetry (following Joseph Bernstein) , Quantum fields and strings: a course for mathematicians, Vol. 1, 2 (Princeton, NJ, 1996/1997), Amer. Math. Soc., Providence, RI, 1999, pp. 41–97
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Raymond F Streater and Arthur S Wightman, PCT, spin and statistics, and all that , Princeton University Press, 2000
2000
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Marcus Berg, Cécile DeWitt-Morette, Shangjr Gwo, and Eric Kramer, The pin groups in physics: C, P and T , Reviews in Mathematical Physics 13
2001
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Ulrich Bunke, Transgression of the index gerbe , Manuscripta Math. 109
2002
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M. J. Hopkins, Algebraic topology and modular forms , Proceedings of the International Congress of Mathematicians, Vol. I (Beijing, 2002) (Beijing), Higher Ed. Press, 2002, pp. 291–317. arXiv:math/0212397
2002
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2012
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by same author, What one can hope to prove about three-dimensional gauge theory . http://scgp.stonybrook.edu/video_portal/video.php?id=563 . Talk at Mathematical Foundations of Quantum Field Theory Workshop , Simons Center for Geometry and Physics, January 2012
2012
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2013
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by same author, The cobordism hypothesis , Bull. Amer. Math. Soc. (N.S.) 50
2013
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2013
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2013
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by same author, On the Classification of Short-Range Entangled States , June, 2013. http://scgp.stonybrook.edu/archives/7874 . Lecture at SCGP
2013
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2014
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2014
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2014
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2014
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by same author, Short range entangled quantum states , May, 2014. lecture at MSRI
2014
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2014
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2014
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2014
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by same author, Homotopy-theoretic approach to SPT phases in action: ℤ / 16 ℤ {\mathbb{Z}}/16{\mathbb{Z}} classification of three-dimensional superconductors , January 2015. http://www.ipam.ucla.edu/abstract/?tid=12389&pcode=STQ2015 . talk at Symmetry and Topology in Quantum Matter , Institute for Pure and Applied Mathematics
2015
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2015
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2016
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M. A. Hill, M. J. Hopkins, and D. C. Ravenel, On the nonexistence of elements of Kervaire invariant one , Ann. of Math. (2) 184
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Edward Witten, Fermion Path Integrals And Topological Phases , Rev. Mod. Phys. 88
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Theo Johnson-Freyd, Spin, statistics, orientations, unitarity , Algebr. Geom. Topol. 17
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2019
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by same author, Lectures on Field Theory and Topology , CBMS Regional Conference Series in Mathematics, vol. 133, American Mathematical Society, 2019
2019
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