Modular invariance, characteristic numbers and $\eta$ invariants

Fei Han; Weiping Zhang

arxiv: math/0305289 · v1 · submitted 2003-05-20 · 🧮 math.DG · hep-th· math.AT

Modular invariance, characteristic numbers and η invariants

Fei Han , Weiping Zhang This is my paper

classification 🧮 math.DG hep-thmath.AT

keywords congruencefinashinformulasalvarez-gaumanalyticapplybundlecancellation

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We generalize the "miraculous cancellation" formulas of Alvarez-Gaum\'e, Witten and Kefeng Liu to a twisted version where an extra complex line bundle is involved. We also apply our result to discuss intrinsic relations between the higher dimensional Rokhlin type congruence formulas of Ochanine [O1], Finashin [F] and Zhang [Z1, 2]. In particular, an analytic proof of the Finashin congruence formula is given.

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Modular invariance, characteristic numbers and η invariants

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