Geometric Galois Actions Volume 2 The Inverse Galois Problem Moduli Spaces And Mapping Class Groups
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Geometric Galois Actions Volume 2 The Inverse Galois Problem Moduli Spaces And Mapping Class Groups
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Author : Leila Schneps
language : de
Publisher: Cambridge University Press
Release Date : 1997-08-07
Geometric Galois Actions Volume 2 The Inverse Galois Problem Moduli Spaces And Mapping Class Groups written by Leila Schneps and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-08-07 with Mathematics categories.
This book surveys progress in the domains described in the hitherto unpublished manuscript "Esquisse d'un Programme" (Sketch of a Program) by Alexander Grothendieck. It will be of wide interest amongst workers in algebraic geometry, number theory, algebra and topology.
Geometric Galois Actions
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Author : Leila Schneps
language : en
Publisher:
Release Date : 1997
Geometric Galois Actions written by Leila Schneps and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Geometry, Algebraic categories.
Moduli Spaces Of Curves Mapping Class Groups And Field Theory
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Author : Groupes Modulaires Et Th'orie Des Espaces De Modules Des Courbes
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Moduli Spaces Of Curves Mapping Class Groups And Field Theory written by Groupes Modulaires Et Th'orie Des Espaces De Modules Des Courbes and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
This book grew out of a workshop on the applications of moduli spaces of Riemann surfaces in theoretical physics and number theory and on Grothendieck's dessins d'enfants and their generalizations. Chapter 1 gives an introduction to Teichmuller space that is more concise than the popular textbooks, yet contains full proofs of many useful results which are often difficult to find in the literature. This chapter also contains an introduction to moduli spaces of curves, with a detailed description of the genus zero case, and in particular of the part at infinity. Chapter 2 takes up the subject of the genus zero moduli spaces and gives a complete description of their fundamental groupoids, based at tangential base points neighboring the part at infinity; the description relies on an identification of the structure of these groupoids with that of certain canonical subgroupoids of a free braided tensor category. It concludes with a study of the canonical Galois action on the fundamental groupoids, computed using Grothendick-Teichmuller theory. Finally, Chapter 3 studies strict ribbon categories, which are closely related to braided tensor categories: here they are used to construct invariants of 3-manifolds which in turn give rise to quantum field theories.
Graphs On Surfaces And Their Applications
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Author : Sergei K. Lando
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Graphs On Surfaces And Their Applications written by Sergei K. Lando and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
Graphs drawn on two-dimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather isolated, has witnessed the appearance of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast field of research. The book provides an accessible introduction to this new domain, including such topics as coverings of Riemann surfaces, the Galois group action on embedded graphs (Grothendieck's theory of "dessins d'enfants"), the matrix integral method, moduli spaces of curves, the topology of meromorphic functions, and combinatorial aspects of Vassiliev's knot invariants and, in an appendix by Don Zagier, the use of finite group representation theory. The presentation is concrete throughout, with numerous figures, examples (including computer calculations) and exercises, and should appeal to both graduate students and researchers.
Arithmetic Fundamental Groups And Noncommutative Algebra
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Author : Michael D. Fried
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Arithmetic Fundamental Groups And Noncommutative Algebra written by Michael D. Fried and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Fundamental groups (Mathematics) categories.
The arithmetic and geometry of moduli spaces and their fundamental groups are a very active research area. This book offers a complete overview of developments made over the last decade. The papers in this volume examine the geometry of moduli spaces of curves with a function on them. The main players in Part 1 are the absolute Galois group $G {\mathbb Q $ of the algebraic numbers and its close relatives. By analyzing how $G {\mathbb Q $ acts on fundamental groups defined by Hurwitz moduli problems, the authors achieve a grand generalization of Serre's program from the 1960s. Papers in Part 2 apply $\theta$-functions and configuration spaces to the study of fundamental groups over positive characteristic fields. In this section, several authors use Grothendieck's famous lifting results to give extensions to wildly ramified covers. Properties of the fundamental groups have brought collaborations between geometers and group theorists. Several Part 3 papers investigate new versions of the genus 0 problem. In particular, this includes results severely limiting possible monodromy groups of sphere covers. Finally, Part 4 papers treat Deligne's theory of Tannakian categories and arithmetic versions of the Kodaira-Spencer map. This volume is geared toward graduate students and research mathematicians interested in arithmetic algebraic geometry.
An Atlas Of The Smaller Maps In Orientable And Nonorientable Surfaces
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Author : David Jackson
language : en
Publisher: CRC Press
Release Date : 2000-09-15
An Atlas Of The Smaller Maps In Orientable And Nonorientable Surfaces written by David Jackson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-09-15 with Computers categories.
Maps are beguilingly simple structures with deep and ubiquitous properties. They arise in an essential way in many areas of mathematics and mathematical physics, but require considerable time and computational effort to generate. Few collected drawings are available for reference, and little has been written, in book form, about their enumerative a
Automorphisms Of Riemann Surfaces Subgroups Of Mapping Class Groups And Related Topics
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Author : Aaron Wootton
language : en
Publisher: American Mathematical Society
Release Date : 2022-02-03
Automorphisms Of Riemann Surfaces Subgroups Of Mapping Class Groups And Related Topics written by Aaron Wootton and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-03 with Mathematics categories.
Automorphism groups of Riemann surfaces have been widely studied for almost 150 years. This area has persisted in part because it has close ties to many other topics of interest such as number theory, graph theory, mapping class groups, and geometric and computational group theory. In recent years there has been a major revival in this area due in part to great advances in computer algebra systems and progress in finite group theory. This volume provides a concise but thorough introduction for newcomers to the area while at the same time highlighting new developments for established researchers. The volume starts with two expository articles. The first of these articles gives a historical perspective of the field with an emphasis on highly symmetric surfaces, such as Hurwitz surfaces. The second expository article focuses on the future of the field, outlining some of the more popular topics in recent years and providing 78 open research problems across all topics. The remaining articles showcase new developments in the area and have specifically been chosen to cover a variety of topics to illustrate the range of diversity within the field.
Around Grothendieck S Esquisse D Un Programme
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Author : Leila Schneps
language : en
Publisher: Cambridge University Press
Release Date : 1997-07-10
Around Grothendieck S Esquisse D Un Programme written by Leila Schneps and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-07-10 with Mathematics categories.
The first of two companion volumes on anabelian algebraic geometry, this book contains the famous, but hitherto unpublished manuscript 'Esquisse d'un Programme' (Sketch of a Program) by Alexander Grothendieck. This work, written in 1984, fourteen years after his retirement from public life in mathematics, together with the closely connected letter to Gerd Faltings, dating from 1983 and also published for the first time in this volume, describe a powerful program of future mathematics, unifying aspects of geometry and arithmetic via the central point of moduli spaces of curves; it is written in an artistic and informal style. The book also contains several articles on subjects directly related to the ideas explored in the manuscripts; these are surveys of mathematics due to Grothendieck, explanations of points raised in the Esquisse, and surveys on progress in the domains described there.
Galois Covers Grothendieck Teichm Ller Theory And Dessins D Enfants
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Author : Frank Neumann
language : en
Publisher: Springer Nature
Release Date : 2020-09-26
Galois Covers Grothendieck Teichm Ller Theory And Dessins D Enfants written by Frank Neumann and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-26 with Mathematics categories.
This book presents original peer-reviewed contributions from the London Mathematical Society (LMS) Midlands Regional Meeting and Workshop on 'Galois Covers, Grothendieck-Teichmüller Theory and Dessinsd'Enfants', which took place at the University of Leicester, UK, from 4 to 7 June, 2018. Within the theme of the workshop, the collected articles cover a broad range of topics and explore exciting new links between algebraic geometry, representation theory, group theory, number theory and algebraic topology. The book combines research and overview articles by prominent international researchers and provides a valuable resource for researchers and students alike.
Decorated Teichm Ller Theory
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Author : R. C. Penner
language : en
Publisher: European Mathematical Society
Release Date : 2012
Decorated Teichm Ller Theory written by R. C. Penner and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Teichmu ller spaces categories.
There is an essentially ``tinker-toy'' model of a trivial bundle over the classical Teichmuller space of a punctured surface, called the decorated Teichmuller space, where the fiber over a point is the space of all tuples of horocycles, one about each puncture. This model leads to an extension of the classical mapping class groups called the Ptolemy groupoids and to certain matrix models solving related enumerative problems, each of which has proved useful both in mathematics and in theoretical physics. These spaces enjoy several related parametrizations leading to a rich and intricate algebro-geometric structure tied to the already elaborate combinatorial structure of the tinker-toy model. Indeed, the natural coordinates give the prototypical examples not only of cluster algebras but also of tropicalization. This interplay of combinatorics and coordinates admits further manifestations, for example, in a Lie theory for homeomorphisms of the circle, in the geometry underlying the Gauss product, in profinite and pronilpotent geometry, in the combinatorics underlying conformal and topological quantum field theories, and in the geometry and combinatorics of macromolecules. This volume gives the story a wider context of these decorated Teichmuller spaces as developed by the author over the last two decades in a series of papers, some of them in collaboration. Sometimes correcting errors or typos, sometimes simplifying proofs, and sometimes articulating more general formulations than the original research papers, this volume is self contained and requires little formal background. Based on a master's course at Aarhus University, it gives the first treatment of these works in monographic form.