Modular Invariance and Twisted Anomaly Cancellations of Characteristic Numbers

Mathematics – Differential Geometry

Scientific paper

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30 pages, new contents added

Scientific paper

By studying modular invariance properties of some characteristic forms, we
obtain twisted anomaly cancellation formulas. We apply these twisted
cancellation formulas to study divisibilities on spin manifolds and congruences
on spin$^c$ manifolds. Especially, we get twisted Rokhlin congruences for
$8k+4$ dimensional spin$^c$ manifolds

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