Mixing and monodromy of abstract polytopes
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- by B. Monson, Daniel Pellicer and Gordon Williams PDF
- Trans. Amer. Math. Soc. 366 (2014), 2651-2681 Request permission
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.References
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Additional Information
- B. Monson
- Affiliation: Department of Mathematics, University of New Brunswick, Fredericton, New Bruns- wick, 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
- MR Author ID: 694060
- Email: giwilliams@alaska.edu
- 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. - © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 366 (2014), 2651-2681
- MSC (2010): Primary 51M20; Secondary 20F55
- DOI: https://doi.org/10.1090/S0002-9947-2013-05954-5
- MathSciNet review: 3165650