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Integer hulls of linear polyhedra and scl in families. (English) Zbl 1300.11100

Summary: 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.

MSC:

11P21 Lattice points in specified regions
11H06 Lattices and convex bodies (number-theoretic aspects)
57M07 Topological methods in group theory
20F65 Geometric group theory
20J05 Homological methods in group theory

Software:

Qhull; scabble; sss
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

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