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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard


IMPACT FACTOR 2018: 0.789

CiteScore 2018: 0.73

SCImago Journal Rank (SJR) 2018: 0.329
Source Normalized Impact per Paper (SNIP) 2018: 0.908

Mathematical Citation Quotient (MCQ) 2018: 0.53

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1615-7168
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Volume 19, Issue 4

Issues

Affine-compact functors

Joseph Gubeladze
  • Corresponding author
  • Department of Mathematics, San Francisco State University, 1600 Holloway Ave., San Francisco, CA 94132, USA
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Published Online: 2019-06-23 | DOI: https://doi.org/10.1515/advgeom-2019-0004

Abstract

Several well known polytopal constructions are examined from the functorial point of view. A naive analogy between the Billera–Sturmfels fiber polytope and the abelian kernel is disproved by an infinite explicit series of polytopes. A correct functorial formula is provided in terms of an affine-compact substitute of the abelian kernel. The dual cokernel object is almost always the natural affine projection. The Mond–Smith–van Straten space of sandwiched simplices, useful in stochastic factorizations, leads to a different kind of affine-compact functors and new challenges in polytope theory.

Keywords: Polytope; fiber polytope; compact set; convex set; affine map; Minkowski sum; representable functor; affine-compact kernel; sandwiched simplices

MSC 2010: Primary 18B30; 52B11; Secondary 52A07; 52A25

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About the article

Received: 2016-11-24

Revised: 2018-04-03

Published Online: 2019-06-23

Published in Print: 2019-10-25


Communicated by: M. Joswig

Funding: Supported by U.S. NSF grant DMS 1301487 and Georgian NSF grant DI/16/5-103/12.


Citation Information: Advances in Geometry, Volume 19, Issue 4, Pages 487–504, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2019-0004.

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