Linfan Mao's Automorphism Groups of Maps, Surfaces and Smarandache PDF

By Linfan Mao

ISBN-10: 1931233926

ISBN-13: 9781931233927

A combinatorial map is a attached topological graph cellularly embedded in a floor. This monograph concentrates at the automorphism team of a map, that's concerning the automorphism teams of a Klein floor and a Smarandache manifold, additionally utilized to the enumeration of unrooted maps on orientable and non-orientable surfaces. a few effects for the automorphism teams of maps, Klein surfaces and Smarandache manifolds and the enumeration of unrooted maps underlying a graph on orientable and non-orientable surfaces are chanced on. An hassle-free class for the closed s-manifolds is located. Open difficulties with regards to the combinatorial maps with the differential geometry, Riemann geometry and Smarandache geometries also are provided during this monograph for the additional functions of the combinatorial maps to the classical arithmetic.

Show description

Read or Download Automorphism Groups of Maps, Surfaces and Smarandache Geometries (Partially Post-Doctoral Research for the Chinese Academy of Sciences) PDF

Similar general & reference books

Get Amino Acids and Peptides (1998) PDF

This article is meant for undergraduate and starting graduate scholars in chemistry and biochemistry learning amino acids and peptides. The authors be aware of amino acids and peptides with out special discussions of proteins, whereas giving the entire crucial heritage chemistry, together with series choice, synthesis and spectroscopic tools.

Download e-book for iPad: Methods of Multivariate Analysis (Wiley Series in by Alvin C. Rencher

Amstat information requested 3 overview editors to fee their best 5 favourite books within the September 2003 factor. equipment of Multivariate research was once between these selected. while measuring numerous variables on a posh experimental unit, it's always essential to learn the variables concurrently, instead of isolate them and view them separately.

Get Biographical Encyclopedia of Scientists, Third Edition PDF

New version of a very popular Reference because the first totally up-to-date model in virtually a decade, this accomplished compendium brings jointly 2400 scientists who've made very important contributions to the vast international of technological know-how. instead of a Who’s-Who variety laundry record, this simple source offers crucial biographical info and makes a speciality of medical success.

Read e-book online Foundations of Organic Chemistry: Unity and Diversity of PDF

This booklet differs from different natural chemistry textbooks in that it's not concentrated in basic terms at the wishes of scholars learning premed, yet relatively for all scholars learning natural chemistry. It directs the reader to query current assumptions instead of to simply accept what's advised, so the moment bankruptcy is basically dedicated to spectroscopy (rather than discovering it a lot in a while as with most modern natural chemistry textbooks).

Extra resources for Automorphism Groups of Maps, Surfaces and Smarandache Geometries (Partially Post-Doctoral Research for the Chinese Academy of Sciences)

Sample text

4. 2 The measures on a map On the classical geometry, its central question is to determine the measures on the objects, such as the distance, angle, area, volume, curvature, . .. For maps being a combinatorial model of Klein surfaces, we also wish to introduce various measures on a map and enlarge its application filed to other branch of mathematics.. 1 The angle on a map For a map M = (Xα,β , P), x ∈ Xα,β , the permutation pair {(x, Px), (αx, P −1 αx)} is called an angle incident with x, which is introduced by Tutte in [66].

By the previous voltage assignment, we also know that M l is a lifting of the quotient map M/G with the voltage assignment ϑ : Xα,β /G → G. Therefore, M ∼ = (M/G)ϑ . This completes the proof. 1, we get the following result for a group to be an automorphism group of a map. 2 If a group G, G |G|(χ(M/G) + AutM, is fixed-free on V (M), then (−1 + m∈O(F (M/G)) 1 )) = χ(M). 1, we know that there is a voltage assignment ϑ on the quotient map M/G such that M ∼ = (M/G)ϑ . 3, we know the Euler characteristic of the map M is χ(M) = |G|(χ(M/G) + (−1 + m∈O(F (M/G)) 1 )).

Case 1 M is orientable. Since χ(M/G) + 1 = (|Φv (g)| + |Φf (g)|) ≥ 0, we know that χ(M/G) ≥ −1. Whence, χ(M/G) = 0 or 2. Therefore, we have that |G| = 1 + χ(M/G) − χ(M) ≤ 3 − χ(M) = 2g(M) + 1. That is, Nmax ≤ 2g(M) + 1. Chapter 2 On the Automorphisms of a Klein Surface and a s-Manifold Case 2 56 M is non-orientable. In this case, since χ(M/G) ≥ −1, we know that χ(M/G) = −1, 0, 1 or 2. Whence, we have that |G| = 1 + χ(M/G) − χ(M) ≤ 3 − χ(M) = g(M) + 1. This completes the proof. 7, which is even more better than the results already known.

Download PDF sample

Automorphism Groups of Maps, Surfaces and Smarandache Geometries (Partially Post-Doctoral Research for the Chinese Academy of Sciences) by Linfan Mao


by Charles
4.0

Rated 4.96 of 5 – based on 10 votes