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1 edition of Subgroups of teichmuller modular groups found in the catalog.

Subgroups of teichmuller modular groups

by Nikolai V. Ivanov

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Published by American Mathematical Soc in [S.l.] .
Written in English


The Physical Object
Paginationp.
ID Numbers
Open LibraryOL27090027M
ISBN 100821819682
ISBN 109780821819685
OCLC/WorldCa785775105

Subgroups of Teichmuller Modular Groups. Häftad. This is the English translation of our introductory book on Teichmiiller space written in Japanese. We have taken advantage of the opportunity afforded by this translation to correct some minor errors in the original text, and to include several new related topics as additional sections. He obtained his Ph.D. under the guidance of Vladimir Abramovich Rokhlin in at the Steklov Mathematical Institute.. According to Google Scholar, on 11 March , Ivanov's works had received 2, citations and his h-index was He is a fellow of the American Mathematical Society since He is the author of the book Subgroups of Teichmüller Modular mater: Steklov Mathematical Institute.

that is a topological group with the discrete topology. The theory of modular forms can be presented for arbitrary discrete groups of SL(2;R) with some additional complications. For more facts about discrete subgroups of SL(2;R), see Shimura’s book. 3 The Fundamental Domain for G In this section, we show that the domain D= fz2Hjjzj 1;jRe(z)j File Size: KB. ] SUBGROUPS OF A FREE PRODUCT OF TWO GROUPS by an edge, generate their amalgamated product. More generally, the factors in any subtree generate their tree product. [Note that the definition, as given by H. Neumann [12], of the generalized free product of groups {A¡} with amalgamated subgroups is the partial generalized.

MATH Homework Solution Han-Bom Moon Homework 4 Solution Chapter 4. all generators of Z 6, Z 8, and Z Z 6, Z 8, and Z 20 are cyclic groups generated by 1. Because jZ 6j= 6, all generators of Z 6 are of the form k 1 = k where gcd(6;k) = 1. So k = 1;5 and there are twoFile Size: KB. 2) Since groups with modular subgroup lattice (also called M-groups) are classified, one can try to implement known criteria for a finite group to be an M-group. 3) Straightforward calculation of subgroups of the group and then checking that the modular law holds. I've implemented (3) in GAP as follows.


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Subgroups of teichmuller modular groups by Nikolai V. Ivanov Download PDF EPUB FB2

The results also include a clear geometric picture of subgroups of modular groups and their action on Thurston's boundary of Teichmuller spaces. Aimed at research mathematicians and graduate students, this book is suitable as supplementary material in advanced graduate courses.

The results also include a clear geometric picture of subgroups of modular groups and their action on Thurston's boundary of Teichmuller spaces.

Aimed at research mathematicians and graduate students, this book is suitable as supplementary material in advanced graduate : Paperback.

Teichmuller modular groups, also known as mapping class groups of surfaces, serve as a meeting ground for several branches of mathematics.

This work focuses mainly on the group-theoretic properties of these groups and their subgroups. Genre/Form: Electronic books: Additional Physical Format: Print version: Ivanov, N.V.

Subgroups of Teichmuller modular groups. Providence, R.I.: American. Teichmuller modular groups, also known as mapping class groups of surfaces, serve as a meeting ground for several branches of mathematics, including low-dimensional topology, the theory of Teichmuller spaces, group theory, and mathematical physics.

The present work focuses mainly on the Price: $ The results also include a clear geometric picture of subgroups of modular groups and their action on Thurston's boundary of Teichmuller spaces.

Aimed at research mathematicians and graduate students, this book is suitable as supplementary material in advanced graduate Range: 6,€ - 7,€.

A subgroup of a group is termed a modular subgroup if it is a modular element in the lattice of subgroups. Explicitly, a subgroup of a group is termed a modular subgroup if for any subgroups and of such that: Relation with other properties Stronger properties.

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 between and () and for a. A subgroup of the Grothendieck-Teichmüller group is f σ (x − 1, y − 1) of Ihara [I1,2], but the difference is not theoretically es- sential except for small alterations of indices in.

Download Citation | Some Remarks on Teichmuller Spaces and Modular Groups | We study the fixed point sets of subgroups of modular groups acting on Teichmüller spaces.

| Find, read and cite all Author: Yun Hu. For a group whose lattice of subgroups is modular, see Iwasawa group. In mathematics, the modular group is the projective special linear group PSL (2, Z) of 2 x 2 matrices with integer coefficients and unit determinant.

The matrices A and -A are identified. The modular group acts on the upper-half of the complex plane by fractional linear. MathematicalResearchLetters10, 97– () GEOMETRIC AND ARITHMETIC SUBGROUPS OF THE GROTHENDIECK-TEICHMULLER GROUP¨ Hidekazu Furusho Abstract.

We compare two geometrically constructed subgroups IΓ and GTK of the Grothendieck-Teichm¨uller group GT with an arithmetically constructed subgroup GTA by deducing arithmetic properties from geometric ones.

We. Subgroups of Teichmüller modular groups and their frattini subgroups. "Algebraic properties of the mapping class groups of surfaces," LOMI Preprints, E, Leningrad (). N.V. Subgroups of Teichmüller modular groups and their frattini Cited by: 8. THE NIELSEN PROBLEM FOR TEICHMULLER MODULAR GROUPS¨ 3 In fact, every finite subgroup ˆΓ of Mod AT(R) can be realized as a subgroup of QCe(R) whose elements are conformal outside some topologically finite sub- surface of finite area in the Riemann surface corresponding to the fixed point.

This book, which grew out of Steven Bleiler's lecture notes from a course given by Andrew Casson at the University of Texas, is designed to serve as an introduction to the applications of hyperbolic geometry to low dimensional topology.

In particular it provides a concise exposition of the work of Neilsen and Thurston on the automorphisms of surfaces. Normal Subgroups of the Modular Group* Leon Greenberg** and Morris Newman Institute for Basic Standards, National Bureau of Standards, Washington, D.C.

Except for the groups f, P, or P, the index of a normal subgroup is a multiple of 6. The commutator subgroup f ' of f is a free group of rank 2, freely generated by.

In this chapter the questions and results of the first chapter for the homogeneous and inhomogeneous modular group will be carried over and extended to its subgroups.

We will restrict ourselves mainly to subgroups of finite index, and turn our particular interest to a special class of subgroups, the so-called congruence : Bruno Schoeneberg.

This result is related to the lattice of subgroups in a group. Statement Symbolic statement. Let, and be subgroups of a group with the property : Note here that denotes the product of subgroups and is not in general a group.

Implications. In case commutes with the groups and, then the above can be recast as saying that the modular identity holds for the lattice of subgroups. An element of a lattice is called modular if, roughly, the modular law holds whenever it is substituted into one of the variables.

Every normal subgroups is a modular element of the subgroup lattice, and more generally every permutable subgroup (a subgroup M with MH=HM for every subgroup H) is a modular element.

The image of a normal subgroup. In this volume boundary value problems are studied from two points of view; solvability, unique or otherwise, and the effect of various smoothness properties of the given functions on the smoothness of the solutions. There are seven chapters contained in this volume.

Chapter One gives a statement of the new results and an historical sketch. For the Love of Physics - Walter Lewin - - Duration: Lectures by Walter Lewin. They will make you ♥ Physics. Recommended for you.JOURNAL OF ALGE () On Modular p-Groups ROBERT W.

VAN DER WAALL Mathematisch Instituut der Katholieke Universiteit te Nijmegen, The Netherlands Communicated by B. Huppert Received Ma INTRODUCTION A modular ji>-group is one whose lattice of subgroups is by: 3.Combinatorial Group Theory and Topology.

(AM), Volume - Ebook written by S. M. Gersten, John R. Stallings. Read this book using Google Play Books app on your PC, android, iOS devices.

Download for offline reading, highlight, bookmark or take notes while you read Combinatorial Group Theory and Topology. (AM), Volume