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.References
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Additional Information
- Danny Calegari
- Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
- Address at time of publication: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
- MR Author ID: 605373
- Email: dannyc@its.caltech.edu, dannyc@math.uchicago.edu
- Alden Walker
- Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
- Address at time of publication: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
- MR Author ID: 925092
- Email: awalker@caltech.edu, akwalker@math.uchicago.edu
- Received by editor(s): November 22, 2010
- Received by editor(s) in revised form: November 29, 2011
- Published electronically: February 26, 2013
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 365 (2013), 5085-5102
- MSC (2010): Primary 11P21, 11H06, 57M07, 20F65, 20J05
- DOI: https://doi.org/10.1090/S0002-9947-2013-05775-3
- MathSciNet review: 3074368