Semi-equivelar maps on the torus and the Klein bottle with few vertices
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Anand Kumar Tiwari
und
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.
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© 2017 Mathematical Institute Slovak Academy of Sciences
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Artikel in diesem Heft
- 10.1515/ms-2015-0200
- Zero-divisor graphs of lower dismantlable lattices I
- Some results on the intersection graph of submodules of a module
- Class number parities of compositum of quadratic function fields
- Examples of beurling prime systems
-
Connection between multiplication theorem for Bernoulli polynomials and first factor
- On permutational invariance of the metric discrepancy results
- Evaluation of sums containing triple aerated generalized Fibonomial coefficients
- Linear algebraic proof of Wigner theorem and its consequences
- A note on groups with finite conjugacy classes of subnormal subgroups
- Groups with the same complex group algebras as some extensions of psl(2, pn)
- Klee-Phelps convex groupoids
- On analytic functions with generalized bounded Mocanu variation in conic domain with complex order
- Weak interpolation for the lipschitz class
- Generalized Padé approximants for plane condenser and distribution of points
- Three-variable symmetric and antisymmetric exponential functions and orthogonal polynomials
- Positive solutions of nonlocal integral BVPS for the nonlinear coupled system involving high-order fractional differential
- Existence of positive solutions for a nonlinear nth-order m-point p-Laplacian impulsive boundary value problem
- Dirichlet boundary value problem for differential equation with ϕ-Laplacian and state-dependent impulses
- On the oscillation of certain third order nonlinear dynamic equations with a nonlinear damping term
- Homoclinic solutions for ordinary (q, p)-Laplacian systems with a coercive potential
- Semi-equivelar maps on the torus and the Klein bottle with few vertices
- A problem considered by Friedlander & Iwaniec and the discrete Hardy-Littlewood method
