Semi-equivelar maps on the torus and the Klein bottle with few vertices
-
Anand Kumar Tiwari
and
Ashish Kumar Upadhyay
Abstract
Semi-equivelar maps are generalizations of maps on the surfaces of Archimedean solids to surfaces other than the 2-sphere. The well known 11 types of normal tilings of the plane suggest the possible types of semi-equivelar maps on the torus and the Klein bottle. In this article we classify (up to isomorphism) semi-equivelar maps on the torus and the Klein bottle with few vertices.
This work was supported by DST-SERB Grant No. SR/S4/MS: 717/10 (acknowledged by Ashish K Upadhyay) and CSIR(SRF) Award No. 09/1023(0003)/1010-EMR-I (acknowledged by Anand K Tiwari).
Acknowledgement
We are thankful to the anonymous referee(s) for her/his suggestions and comments which enlightened and educated us on the subject and presentation of the work. This lead to significant improvements in the content and presentation of the article. Geometric arguments in Remark 1 were also suggested by the referee. Part of this work was completed when the second author was visiting Indian Institute of Science. We would like to thank Prof. B. Datta for his support.
References
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© 2017 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- 10.1515/ms-2015-0200
- Zero-divisor graphs of lower dismantlable lattices I
- Some results on the intersection graph of submodules of a module
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Connection between multiplication theorem for Bernoulli polynomials and first factor
- On permutational invariance of the metric discrepancy results
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- Groups with the same complex group algebras as some extensions of psl(2, pn)
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