Integer hulls of linear polyhedra and scl in families

Calegari, Danny; Walker, Alden

doi:10.1090/S0002-9947-2013-05775-3

Integer hulls of linear polyhedra and scl in families
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by Danny Calegari and Alden Walker PDF

Trans. Amer. Math. Soc. 365 (2013), 5085-5102 Request permission

Abstract:

The integer hull of a polyhedron is the convex hull of the integer points contained in it. We show that the vertices of the integer hulls of a rational family of polyhedra of size $O(n)$ have eventually quasipolynomial coordinates. As a corollary, we show that the stable commutator length of elements in a surgery family is eventually a ratio of quasipolynomials, and that unit balls in the scl norm eventually quasiconverge in finite-dimensional surgery families.

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