Last edited by Bragar
Saturday, August 1, 2020 | History

2 edition of Seifert manifolds and Fuchsian groups. found in the catalog.

Seifert manifolds and Fuchsian groups.

Ayoub Barasm-Mamagani

# Seifert manifolds and Fuchsian groups.

## by Ayoub Barasm-Mamagani

Written in English

Edition Notes

Thesis (Ph.D)-University of Birmingham, Dept of Pure Mathematics.

ID Numbers
Open LibraryOL13737942M

A triangle of groups is a simple complex of groups consisting of a triangle with vertices A, B, are groups Γ A, Γ B, Γ C at each vertex ; Γ BC, Γ CA, Γ AB for each edge ; Γ ABC for the triangle itself.; There is an injective homomorphisms of Γ ABC into all the other groups and of an edge group Γ XY into Γ X and Γ three ways of mapping Γ ABC into a vertex group all . Handbook of Knot Theory. Book • Edited by: William Menasco and Morwen Thistlethwaite. Browse book content. The chapter illustrates ways in which structure first discovered in the braid groups generalizes to structure in Garside groups, Artin groups and surface mapping class groups. This book is a survey of current topics in the.

A modern reference would be Beardon's book on discrete groups or, more generally, Ratcliffe's book on hyperbolic manifolds. $\endgroup$ – Moishe Kohan Mar 16 at 1 $\begingroup$ The key words you want are "Poincare polygon theorem", or . Fuchsian, quasifuchsian, and accidental surfaces Fibers and semiﬁbers Exercises between the fundamental groups of two closed hyperbolic 3-manifolds, then there is an isometry taking one to the other. Prasad extended this work to book is an introduction to the mathematics involved. PrefaceFile Size: 5MB.

of 3-manifolds covered by Lie groups, based on the theory of Seifert ﬁbrations. It turns out that the only nontrivial knot obtained as a coset of the simple group PSL2(R) is the trefoil knot, and the corresponding discrete group is none other than the modular group, so we have S3 \K2,3 ∼= PSL2(R)/PSL2(Z). Possible topics for the final project Below is a list of some ideas I had for final project topics. You should feel free to come up with your own ideas as well. I have not included references here, but I can provide you personally (or by e-mail) references for any of these topics. Some important dates to keep in mind.

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### Seifert manifolds and Fuchsian groups by Ayoub Barasm-Mamagani Download PDF EPUB FB2

This has led, by work of the second author with J. Schultens (see [19] and [26]), to a classification of minimal genus Heegaard splittings in a large class of Seifert fibered spaces, excluding. Representations of free Fuchsian groups in complex hyperbolic space Article in Topology 39(1) January with 15 Reads How we measure 'reads'.

may be seen as a culmination of the work on 3-manifold groups in the last half-century. We conclude the book with a discussion of some outstanding open problems in the theory of 3-manifold groups (in Chapter 7).

What this book is not about. As with any book, this one re ects the tastes and biases of the authors. According to Orlik's lecture notes on Seifert manifolds (and the Wikipedia page on Seifert fiber spaces), a mapping torus over a 2-torus is a Seifert manifold if and only if it is the mapping torus of a mapping with trace less than or equal to 2 in absolute value (under the usual identification $\text{MCG}(T^2) \cong \text{SL}(2,\mathbb{Z})$).

Fuchsian groups Centralizers in Seifert ﬁbered spaces The examples in this chapter were mostly taken from the book Chapter 2. Seifert ﬁbered spaces are 3-manifolds that are unions of pairwise disjoint cir-cles.

There will be restrictions on how the circles ﬁt together. These restrictionsFile Size: KB. fundamental groups of Haken 3-manifolds, e.g., the solution to the word problem. (3)The Jaco{Shalen{Johannson (JSJ) decomposition [JS79, Jon79] of an irre-ducible 3-manifold with incompressible boundary gave insight into the sub-group structure of the fundamental groups of Haken 3-manifolds and pre g-ured Thurston’s Geometrization Conjecture.

In the mathematical disciplines of topology, geometry, and geometric group theory, an orbifold (for "orbit-manifold") is a generalization of a is a topological space (called the underlying space) with an orbifold structure (see below).

The underlying space locally looks like the quotient space of a Euclidean space under the linear action of a finite group. Jaco W.H., Shalen P.B.

Seifert fibered spaces in 3-manifolds (AMS, )(ISBN )(T)(s). Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields.

It only takes a minute to sign up. Dirichlet Domain of a Fuchsian Group. Ask Question Asked 6 years, Seifert manifolds and Fuchsian group.

COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle.

ISBN: OCLC Number: Description: xiii, pages: illustrations ; 25 cm. Contents: 1. Geometric Structures 1 (X, G)-structures on manifolds 1 Conformal geometry on the sphere 4 The hyperbolic space H[superscript n] 11 Lie subgroups of the Mobius group 19 Structure developments and holonomy. Quasi-Fuchsian surface subgroups of in nite covolume Kleinian groups by Alvin Jay Kerber Doctor of Philosophy in Mathematics University of California, Berkeley Professor Ian Agol, Chair Given a complete hyperbolic 3-manifold N, one can ask whether its fundamental group = ˇ 1N contains any quasi-Fuchsian surface subgroups.

Equivalently, given a File Size: 1MB. This book introduces and explains hyperbolic geometry and hyperbolic 3- and 2-dimensional manifolds in the first two chapters and then goes on to develop the subject. The author discusses the profound discoveries of the astonishing features of these 3-manifolds, helping the reader to understand them without going into long, detailed formal by: 6.

Seifert Fibered Spaces in Three Manifolds: Memoirs Series No. | W. Jaco, P. Shalen | download | B–OK. Download books for free. Find books. Fuchsian groups. Any Fuchsian group (a discrete subgroup of SL(2, R)) is a Kleinian group, and conversely any Kleinian group preserving the real line (in its action on the Riemann sphere) is a Fuchsian group.

More generally, every Kleinian group preserving a circle or straight line in the Riemann sphere is conjugate to a Fuchsian group. The first reference book on the subject originated in the annotated notes that the young student Seifert took during the courses of algebraic topology given by Threlfall.

InSeifert introduces a particular class of 3-manifolds, known as Seifert manifolds or Seifert fiber spaces. They have been since widely studied, well understood, and Cited by: 4. Kamishima, Conformally flat 3-manifolds with compact automorphism groups, Preprint, to appear in London Math.

Google Scholar [9] Y. Kamishima, Conformally flat manifolds whose development maps are not surjective, Trans. Amer. Math. (), –Author: Yoshinobu Kamishima. The author also gives a brief taste of Fuchsian groups. Chapter 2 is devoted completely to the group theory of graphs, as a warm up to the study of the fundamental group in the next chapter.

The fundamental group is defined to be an equivalence class of maps, and with the exception of the circle, it is calculated using deformation retraction Cited by: [Th3] W. Thurston, 'Hyperbolic structures on 3-manifolds II: Surface groups and 3-manifolds whic fiber over the circle', unpublished preprint.

[Th4] W. Thurston, A norm for the homology of 3-manifolds, Memoirs of the Amer. Math. Soc. 33 (), Cited by: 1. 'How Groups Grow is an excellent introduction to growth of groups for everybody interested in this subject.

It also touches a variety of adjacent subjects (such as amenability, isoperimetric inequalities, groups generated by automata, etc.) It is written in a very accessible style, with very clear exposition of all main results.'Cited by: 2.

book [23] Surfaces and discontinuous groups; the book [19], Later on an analogue of this statement was found for Fuchsian groups. This generalization of the Nielsen theorem remained the best in the 's until. examples were given of Seifert manifolds, the geometric rank of whose fundamentalAuthor: A A Mal'tsev, S P Novikov, A V Zarelua.M.

Boileau and H. Zieschang, Heegard genus of closed orientable Seifert manifolds, Invent. Math. 76 (), – Math. 76 (), – MathSciNet CrossRef zbMATH Google ScholarCited by: BIBLIOGRAPHY [Bonahon, ] Bonahon, F.

(). Low-dimensional geometry, volume 49 of Student Mathematical Library. American Mathematical Society, Providence, RI; Institute forFile Size: KB.