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Published February 26, 2013 | Submitted + Published
Journal Article Open

Integer hulls of linear polyhedra and scl in families

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.

Additional Information

© 2013 American Mathematical Society The copyright for this article reverts to public domain 28 years after publication. Received by the editors November 22, 2010 and, in revised form, November 29, 2011. Article electronically published on February 26, 2013. The first author was supported by NSF grant DMS 1005246. The authors thank Jesus De Loera and Greg Kuperberg for some useful conversations about this material. The authors also thank the anonymous referees for helpful suggestions and corrections.

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Published - S0002-9947-2013-05775-3.pdf

Submitted - 1011.1455v3.pdf

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