Galois Covers, Grothendieck-Teichmüller Theory and Dessins d'Enfants
Title | Galois Covers, Grothendieck-Teichmüller Theory and Dessins d'Enfants PDF eBook |
Author | Frank Neumann |
Publisher | Springer Nature |
Total Pages | 240 |
Release | 2020-09-26 |
Genre | Mathematics |
ISBN | 3030517950 |
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.
The Grothendieck Theory of Dessins D'Enfants
Title | The Grothendieck Theory of Dessins D'Enfants PDF eBook |
Author | Leila Schneps |
Publisher | Cambridge University Press |
Total Pages | 384 |
Release | 1994-07-28 |
Genre | Mathematics |
ISBN | 9780521478212 |
Dessins d'Enfants are combinatorial objects, namely drawings with vertices and edges on topological surfaces. Their interest lies in their relation with the set of algebraic curves defined over the closure of the rationals, and the corresponding action of the absolute Galois group on them. The study of this group via such realted combinatorial methods as its action on the Dessins and on certain fundamental groups of moduli spaces was initiated by Alexander Grothendieck in his unpublished Esquisse d'un Programme, and developed by many of the mathematicians who have contributed to this volume. The various articles here unite all of the basics of the subject as well as the most recent advances. Researchers in number theory, algebraic geometry or related areas of group theory will find much of interest in this book.
Knots and Primes
Title | Knots and Primes PDF eBook |
Author | Masanori Morishita |
Publisher | Springer Nature |
Total Pages | 268 |
Release | |
Genre | |
ISBN | 9819992559 |
Algebra and Galois Theories
Title | Algebra and Galois Theories PDF eBook |
Author | Régine Douady |
Publisher | Springer Nature |
Total Pages | 462 |
Release | 2020-07-13 |
Genre | Mathematics |
ISBN | 3030327965 |
Galois theory has such close analogies with the theory of coverings that algebraists use a geometric language to speak of field extensions, while topologists speak of "Galois coverings". This book endeavors to develop these theories in a parallel way, starting with that of coverings, which better allows the reader to make images. The authors chose a plan that emphasizes this parallelism. The intention is to allow to transfer to the algebraic framework of Galois theory the geometric intuition that one can have in the context of coverings. This book is aimed at graduate students and mathematicians curious about a non-exclusively algebraic view of Galois theory.
Handbook of Teichmüller Theory
Title | Handbook of Teichmüller Theory PDF eBook |
Author | Athanase Papadopoulos |
Publisher | European Mathematical Society |
Total Pages | 888 |
Release | 2007 |
Genre | Mathematics |
ISBN | 9783037190555 |
This multi-volume set deals with Teichmuller theory in the broadest sense, namely, as the study of moduli space of geometric structures on surfaces, with methods inspired or adapted from those of classical Teichmuller theory. The aim is to give a complete panorama of this generalized Teichmuller theory and of its applications in various fields of mathematics. The volumes consist of chapters, each of which is dedicated to a specific topic. The volume has 19 chapters and is divided into four parts: The metric and the analytic theory (uniformization, Weil-Petersson geometry, holomorphic families of Riemann surfaces, infinite-dimensional Teichmuller spaces, cohomology of moduli space, and the intersection theory of moduli space). The group theory (quasi-homomorphisms of mapping class groups, measurable rigidity of mapping class groups, applications to Lefschetz fibrations, affine groups of flat surfaces, braid groups, and Artin groups). Representation spaces and geometric structures (trace coordinates, invariant theory, complex projective structures, circle packings, and moduli spaces of Lorentz manifolds homeomorphic to the product of a surface with the real line). The Grothendieck-Teichmuller theory (dessins d'enfants, Grothendieck's reconstruction principle, and the Teichmuller theory of the solenoid). This handbook is an essential reference for graduate students and researchers interested in Teichmuller theory and its ramifications, in particular for mathematicians working in topology, geometry, algebraic geometry, dynamical systems and complex analysis. The authors are leading experts in the field.
Geometric Galois Actions: Volume 2, The Inverse Galois Problem, Moduli Spaces and Mapping Class Groups
Title | Geometric Galois Actions: Volume 2, The Inverse Galois Problem, Moduli Spaces and Mapping Class Groups PDF eBook |
Author | Leila Schneps |
Publisher | Cambridge University Press |
Total Pages | 363 |
Release | 1997-08-07 |
Genre | Mathematics |
ISBN | 0521596416 |
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.
Galois Groups and Fundamental Groups
Title | Galois Groups and Fundamental Groups PDF eBook |
Author | Leila Schneps |
Publisher | Cambridge University Press |
Total Pages | 486 |
Release | 2003-07-21 |
Genre | Mathematics |
ISBN | 9780521808316 |
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