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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

   

 

Integer hulls of linear polyhedra and scl in families


Authors: Danny Calegari and Alden Walker
Journal: Trans. Amer. Math. Soc. 365 (2013), 5085-5102
MSC (2010): Primary 11P21, 11H06, 57M07, 20F65, 20J05
Published electronically: February 26, 2013
MathSciNet review: 3074368
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Abstract | References | Similar Articles | Additional Information

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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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
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
Email: awalker@caltech.edu, akwalker@math.uchicago.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05775-3
Received by editor(s): November 22, 2010
Received by editor(s) in revised form: November 29, 2011
Published electronically: February 26, 2013
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.



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