Miraculous Cancellation and Pick's Theorem

Details Miraculous Cancellation and Pick's Theorem Miraculous Cancellation and Pick's Theorem

2007-10-03

arxiv.org/abs/0710.0828v1

Mathematics

Geometric Topology

16 pages

Scientific paper

We show that the Cappell-Shaneson version of Pick's theorem for simple lattice polytopes is a consequence of a general relation between characteristic numbers of virtual submanifolds dual to the characteristic classes of a stably almost complex manifold. This relation is analogous to the miraculous cancellation formula of Alvarez-Gaume and Witten, and is imposed by the action of the Landweber-Novikov algebra in the complex cobordism ring of a point.

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