Miraculous Cancellation and Pick's Theorem
K.E. Feldman

TL;DR
This paper links Pick's theorem for lattice polytopes to a broader topological relation involving characteristic classes and cobordism, revealing a deep connection between combinatorics and topology.
Contribution
It demonstrates that Cappell-Shaneson's version of Pick's theorem follows from a general topological relation derived from the action of the Landweber-Novikov algebra.
Findings
Pick's theorem is a consequence of characteristic number relations.
A topological framework explains combinatorial lattice polytope properties.
The relation is analogous to the miraculous cancellation formula.
Abstract
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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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Mathematical Identities · Mathematics and Applications
