Consistency of M-Theory on nonorientable manifolds

Daniel S. Freed, Michael J. Hopkins

备注：: 68 pages, 2 figures; v2 added appendix about cohomology of relevant Thom spectrum plus small changes; v3 added appendix about spin bordism in dimension 12 plus numerous small changes for publication in Quaterly Journal of Mathematics; v4 fixed title on arXiv

英文摘要：

We prove that there is no parity anomaly in M-theory in the low-energy field theory approximation. Our approach is computational. We determine generators for the 12-dimensional bordism group of pin manifolds with a w_1-twisted integer lift of w_4; these are the manifolds on which Wick-rotated M-theory exists. The anomaly cancellation comes down to computing a specific eta-invariant and cubic form on these manifolds. Of interest beyond this specific problem are our expositions of: computational techniques for eta-invariants, the algebraic theory of cubic forms, Adams spectral sequence techniques, and anomalies for spinor fields and Rarita-Schwinger fields.

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