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We prove that there is no parity anomaly in M-theory in the low-energy field theory approximation.
1909
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1958
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John W. Milnor and Michel A. Kervaire, Bernoulli numbers, homotopy groups, and a theorem of Rohlin , Proc. Internat. Congress Math. 1958, Cambridge Univ. Press, New York, 1960, pp. 454–458
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1963
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D. W. Anderson, E. H. Brown, Jr., and F. P. Peterson, Spin cobordism , Bull. Amer. Math. Soc. 72
1966
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by same author, SU {\rm SU} -cobordism, KO {\rm KO} -characteristic numbers, and the Kervaire invariant , Ann. of Math. (2) 83
1966
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by same author, The structure of the Spin cobordism ring , Ann. of Math. (2) 86
1967
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R. T. Seeley, Complex powers of an elliptic operator , Singular Integrals (Proc. Sympos. Pure Math., Chicago, Ill., 1966), Amer. Math. Soc., Providence, R.I., 1967, pp. 288–307
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1972
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J.-P. Serre, A course in arithmetic , Springer-Verlag, New York-Heidelberg, 1973. Translated from the French, Graduate Texts in Mathematics, No. 7
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M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian geometry. I , Math. Proc. Cambridge Philos. Soc. 77
1975
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by same author, Spectral asymmetry and Riemannian geometry. II , Math. Proc. Cambridge Philos. Soc. 78
1975
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by same author, Spectral asymmetry and Riemannian geometry. III , Math. Proc. Cambridge Philos. Soc. 79
1976
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E. H. Brown and M. Comenetz, Pontrjagin duality for generalized homology and cohomology theories , Amer. J. Math. 98
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Harold Donnelly, Eta invariants for G G -spaces , Indiana Univ. Math. J. 27
DJ Benson and Jay A Wood, Integral invariants and cohomology of B Spin ( n ) B\!\Spin(n) , Topology 34
1995
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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
1995
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M. J. Duff, James T. Liu, and R. Minasian, Eleven-dimensional origin of string-string duality: A One loop test , Nucl. Phys. B452
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Cumrun Vafa and Edward Witten, A One loop test of string duality , Nucl. Phys. B447
1995
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Edward Witten, On flux quantization in M M -theory and the effective action , J. Geom. Phys. 22
1997
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1978
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Peter B. Gilkey, The eta invariant for even-dimensional PIN c {\rm PIN}_{{\rm c}} manifolds , Adv. in Math. 58
1985
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D. Quillen, Determinants of Cauchy-Riemann operators on Riemann surfaces , Funktsional. Anal. i Prilozhen. 19
1985
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Akira Kono, On the integral cohomology of B Spin ( n ) B{\rm Spin}(n) , J. Math. Kyoto Univ. 26
1986
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R. E. Stong, Appendix: calculation of Ω 11 Spin ( K ( Z , 4 ) ) \Omega^{{\rm Spin}}_{11}(K(Z,4)) , Workshop on unified string theories (Santa Barbara, Calif., 1985), World Sci. Publishing, Singapore, 1986, pp. 430–437
1986
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Stephan Stolz, Exotic structures on 4-manifolds detected by spectral invariants , Inventiones mathematicae 94
1988
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Andrzej Kozlowski, Transfers in the group of multiplicative units of the classical cohomology ring and Stiefel-Whitney classes , Publ. Res. Inst. Math. Sci. 25
1989
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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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Dominic D. Joyce, Compact manifolds with special holonomy , Oxford Mathematical Monographs, Oxford University Press, Oxford, 2000
2000
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Daniel S. Freed, K K -theory in quantum field theory , Current developments in mathematics, 2001, Int. Press, Somerville, MA, 2002, pp. 41–87. arXiv:math-ph/0206031
2002
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Daniel S. Freed and Jerome A. Jenquin, Appendix: The partition function of the Rarita-Schwinger field (in K K
2002
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G. B. Segal, The definition of conformal field theory , Topology, geometry and quantum field theory, London Math. Soc. Lecture Note Ser., vol. 308, Cambridge Univ. Press, Cambridge, 2004, pp. 421–577
2004
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M. J. Hopkins and I. M. Singer, Quadratic functions in geometry, topology, and M-theory , J. Diff. Geom. 70
2005
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Daniel S. Freed and Gregory W. Moore, Setting the quantum integrand of M-theory , Comm. Math. Phys. 263
2006
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Emanuel Diaconescu, Gregory Moore, and Daniel S. Freed, The M-theory 3-form and E 8 E_{8} gauge theory , Elliptic cohomology, London Math. Soc. Lecture Note Ser., vol. 342, Cambridge Univ. Press, Cambridge, 2007, pp. 44–88. arXiv:hep-th/0312069
2007
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2014
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Manifold Atlas: Spin Bordism , May 2014. http://www.map.mpim-bonn.mpg.de/Spin_bordism
2014
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D. S. Freed, Lectures on Field Theory and Topology , CBMS Regional Conference Series in Mathematics, no. 133, American Mathematical Society, 2019
2019
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