9 edition of **Finite groups of mapping classes of surfaces** found in the catalog.

- 76 Want to read
- 4 Currently reading

Published
**1981**
by Springer-Verlag in Berlin, New York
.

Written in English

- Manifolds (Mathematics),
- Mappings (Mathematics),
- Finite groups.,
- Surfaces.

**Edition Notes**

Statement | Heiner Zieschang. |

Series | Lecture notes in mathematics ;, 875, Lecture notes in Mathematics (Springer-Verlag) ;, 875. |

Classifications | |
---|---|

LC Classifications | QA3 .L28 vol. 875, QA613.2 .L28 vol. 875 |

The Physical Object | |

Pagination | viii, 340 p. : |

Number of Pages | 340 |

ID Numbers | |

Open Library | OL4267523M |

ISBN 10 | 0387108572 |

LC Control Number | 81013531 |

"Representations of surface groups with finite mapping class group orbits." Joint with Indranil Biwas, Mahan Mj, and Ramanujan Santharoubane. (New York J. Math. 24 (), ) pdf NYJM link. "Irreducibility of quantum representations of mapping class groups with boundary." Joint with Ramanujan Santharoubane. Kim, Byung Chun (Inha University) Embedding of braid group into mapping class group induced by 3-fold covering A function from configuration space to moduli space of surface may induce a homomorphism between their fundamental groups which are braid gorups and mapping class groups of surface, respectively. In the analysis of them, we should deal.

The same arguments apply to finite groups, although in this case the graphs are finite, and so quasi-equivalent to trivial graphs (i.e. the graph with one vertex and no edges), and geometric group theory has nothing more to say. From this point of view, finite groups are, in a very precise sense, virtually trivial. Some problems on mapping class groups and moduli space Benson Farb ∗ J Abstract This paper presents a number of problems about mapping class groups and moduli space. The paper will appear in the book Problems on Mapping Class Groups and Related Topics, ed. by B. Farb, Proc. Symp. Pure Math. series, Amer. Math. Soc. Contents 1.

In the last chapter of the book, the author discusses the characteristic classes of surface bundles, where the genus of the surface is greater than or equal to 2. String theorists will appreciate the discussion, as it goes into the mapping class group of surfaces, the Teichmuller modular group, and how they act on the homology group of by: Therefore, one of the fundamental ways to understand the mapping class group is to understand what it does to isotopy classes of curves on your surface. In fact, the essential closed curves inside surfaces determine many geometric properties of the surface. And the mapping class group is the thing that moves isotopy classes of these curves around.

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Finite Groups of Mapping Classes of Surfaces. Authors; Heiner Zieschang; Book. 25 Citations; On finite groups of mapping classes of 3-manifolds: Some applications.

Back Matter. Pages PDF. About this book. Keywords. Finite Groups Nielsensches Realisierungsproblem Riemann surface Surfaces boundary element method construction. Tori, crystallographic groups and the realization of mapping classes.- Marked Riemann surfaces and Fuchsian groups and Fenchel's realization theorem.- Finite groups of mapping classes of surfaces book Nielsen construction of finite groups of mapping classes.- On the Nielsen realization problem.- On finite groups of mapping classes of 3-manifolds: Some applications.

Series Title. Finite Groups of Mapping Classes of Surfaces (Lecture Notes in Mathematics) st Edition. by Heiner Zieschang (Author) › Visit Amazon's Heiner Zieschang Page.

Find all the books, read about the author, and more. See search results for this author. Are you an author. Author: Heiner Zieschang.

Finite Groups of Mapping Classes of Surfaces. It seems that you're in USA. We have a dedicated site for USA. Search Buy this book eB09 € The Nielsen construction of finite groups of mapping classes.

Pages The mapping class groups of surfaces have been heavily studied, and are sometimes called Teichmüller modular groups (note the special case of above), since they act on Teichmüller space and the quotient is the moduli space of Riemann surfaces homeomorphic to the surface.

These groups exhibit features similar both to hyperbolic groups and to higher rank linear. Finite Groups of Mapping Classes of Surfaces (Lecture Notes in Mathematics) [PDF] Structure Theory for Canonical Classes of Finite Groups - Removed; [PDF] Finite Groups of Lie Type: Conjugacy Classes and Complex Characters (Wiley Classics Library) [PDF] Characteristic Classes and the Cohomology of.

A finite presentation of MCG g in the Humphries generators was given by Wajnryb. In this paper we show how to write finite groups of mapping classes in terms of the Humphries generators.

The mapping class group MCG g acts on the Teichmüller space T g of closed Riemann surfaces of genus g as the (holomorphic) automorphism group (Royden).Cited by: 2.

Zieschang H. () On finite groups of mapping classes of 3-manifolds: Some applications. In: Finite Groups of Mapping Classes of Surfaces.

Lecture Notes in Mathematics, vol Author: Heiner Zieschang. Braid groups can be defined as the mapping class groups of a disc with punctures. More precisely, the braid group on n strands is naturally isomorphic to the mapping class group of a disc with n punctures.

The Dehn–Nielsen–Baer theorem. If is closed and is a homeomorphism of then we can define an automorphism ∗ of the fundamental group (,) as follows: fix a path. The central extension of the mapping class groups of punctured surfaces of finite type that arises in quantum Teichm\"uller theory is 12 times the Meyer.

We obtain a finite set of generators for the mapping class group of a nonorientable surface with punctures. We then compute the first homology group of the mapping class group and certain Author: Mustafa Korkmaz. The book then introduces Teichmüller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms.

Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification. Finite-order Mapping Classes versus Finite-order Homeomorphisms Orbifolds, the 84(g −1) Theorem, and the 4g +2Theorem Realizing Finite Groups as Isometry Groups Conjugacy Classes of Finite Subgroups Generating the Mapping Class Group with Torsion 8.

The Dehn–Nielsen–Baer Theorem File Size: 2MB. Groups are one of the simplest and most prevalent algebraic objects in physics. Geometry, which forms the foundation of many physical models, is concerned with spaces and structures that are preserved under transformations of these spaces.

This talk will be about modular representations in finite characteristic of mapping class groups of surfaces coming from the theory of Integral SO(3) Topological Quantum Field Theory. These representations were used in joint work with Reid which will.

Book Description: The study of the mapping class group Mod(S) is a classical topic that is experiencing a lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained.

I am trying to understand the behavior of finite order mapping classes for surfaces of genus g>=2. After fiddling for a while I started to think that no finite order mapping class commutes with any Dehn twist for g>=2.

Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange. A Primer on Mapping Class Groups (henceforth, the Primer) was circulated in preprint form by its authors for several years before its the time it was actually in print, it had already become the standard reference. We consider the Goeritz groups of the Heegaard splittings induced from twisted book decompositions.

We show that there exist Heegaard splittings of distance 2 that have the infinite-order mapping class groups whereas that are not induced from open book decompositions.

Explicit computation of those mapping class groups are : Daiki Iguchi, Yuya Koda. Heiner Zieschang (born 12 November in Kiel; died 5 April ) was a German was a professor at Ruhr-University Bochum from till In he was made an honorary doctor of the University of Toulouse and in he was an honorary professor of Moscow State University.

Literature. Heiner Zieschang: Flächen und ebene .This book covers the following topics: Algebraic Nahm transform for parabolic Higgs bundles on P1, Computing HF by factoring mapping classes, topology of ending lamination space, Asymptotic behaviour and the Nahm transform of doubly periodic instantons with square integrable curvature, FI-modules over Noetherian rings, Hyperbolicity in.The Mathematical Sciences Research Institute (MSRI), founded inis an independent nonprofit mathematical research institution whose funding sources include the National Science Foundation, foundations, corporations, and more than 90 universities and institutions.

The Institute is located at 17 Gauss Way, on the University of California, Berkeley campus, close to .