The Newton Polygon of a Recurrence Sequence of Polynomials and Its Role in Tqft
نویسنده
چکیده
The paper contains a combinatorial theorem (the sequence of Newton polygons of a reccurent sequence of polynomials is quasi-linear) and two applications of it in classical and quantum topology, namely in the behavior of the A-polynomial and a fixed quantum invariant (such as the Jones polynomial) under filling. Our combinatorial theorem, which complements results of Calegari-Walker [CW10] and the author [Gar11a], occupies the bulk of the paper and its proof requires the Lech-Mahler-Skolem theorem of p-adic analytic number theory combined with basic principles in polyhedral and tropical geometry.
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