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

 

Mixing and monodromy of abstract polytopes


Authors: B. Monson, Daniel Pellicer and Gordon Williams
Journal: Trans. Amer. Math. Soc. 366 (2014), 2651-2681
MSC (2010): Primary 51M20; Secondary 20F55
Published electronically: November 4, 2013
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Abstract: The monodromy group $ \mathrm {Mon}(\mathcal {P})$ of an $ n$-polytope $ \mathcal {P}$ encodes the combinatorial information needed to construct $ \mathcal {P}$. By applying tools such as mixing, a natural group-theoretic operation, we develop various criteria for $ \mathrm {Mon}(\mathcal {P})$ itself to be the automorphism group of a regular $ n$-polytope $ \mathcal {R}$. We examine what this can say about regular covers of $ \mathcal {P}$, study a peculiar example of a $ 4$-polytope with infinitely many distinct, minimal regular covers, and then conclude with a brief application of our methods to chiral polytopes.


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Additional Information

B. Monson
Affiliation: Department of Mathematics, University of New Brunswick, Fredericton, New Brunswick, Canada
Email: bmonson@unb.ca

Daniel Pellicer
Affiliation: Instituto de Matematicas, UNAM Morelia, Morelia, Michoacán, México
Email: pellicer@matmor.unam.mx

Gordon Williams
Affiliation: Department of Mathematics, University of Alaska Fairbanks, Fairbanks, Alaska 99775
Email: giwilliams@alaska.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05954-5
PII: S 0002-9947(2013)05954-5
Received by editor(s): June 19, 2012
Received by editor(s) in revised form: September 6, 2012
Published electronically: November 4, 2013
Additional Notes: The first author was supported by NSERC of Canada Discovery Grant # 4818.
The second author was supported by grants PAPIIT (IAOCD) # IA101311 and PAPIIT #IB100312.
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.