Advances in Two-Dimensional Homotopy and Combinatorial Group Theory
Title | Advances in Two-Dimensional Homotopy and Combinatorial Group Theory PDF eBook |
Author | Wolfgang Metzler |
Publisher | Cambridge University Press |
Pages | 193 |
Release | 2018 |
Genre | Mathematics |
ISBN | 1316600904 |
Presents the current state of knowledge in all aspects of two-dimensional homotopy theory. Useful for both students and experts.
Two-Dimensional Homotopy and Combinatorial Group Theory
Title | Two-Dimensional Homotopy and Combinatorial Group Theory PDF eBook |
Author | Cynthia Hog-Angeloni |
Publisher | Cambridge University Press |
Pages | 428 |
Release | 1993-12-09 |
Genre | Mathematics |
ISBN | 0521447003 |
Basic work on two-dimensional homotopy theory dates back to K. Reidemeister and J. H. C. Whitehead. Much work in this area has been done since then, and this book considers the current state of knowledge in all the aspects of the subject. The editors start with introductory chapters on low-dimensional topology, covering both the geometric and algebraic sides of the subject, the latter including crossed modules, Reidemeister-Peiffer identities, and a concrete and modern discussion of Whitehead's algebraic classification of 2-dimensional homotopy types. Further chapters have been skilfully selected and woven together to form a coherent picture. The latest algebraic results and their applications to 3- and 4-dimensional manifolds are dealt with. The geometric nature of the subject is illustrated to the full by over 100 diagrams. Final chapters summarize and contribute to the present status of the conjectures of Zeeman, Whitehead, and Andrews-Curtis. No other book covers all these topics. Some of the material here has been used in courses, making this book valuable for anyone with an interest in two-dimensional homotopy theory, from graduate students to research workers.
Integrable Systems and Algebraic Geometry: Volume 2
Title | Integrable Systems and Algebraic Geometry: Volume 2 PDF eBook |
Author | Ron Donagi |
Publisher | Cambridge University Press |
Pages | 537 |
Release | 2020-04-02 |
Genre | Mathematics |
ISBN | 1108805337 |
Created as a celebration of mathematical pioneer Emma Previato, this comprehensive second volume highlights the connections between her main fields of research, namely algebraic geometry and integrable systems. Written by leaders in the field, the text is accessible to graduate students and non-experts, as well as researchers.
Permutation Groups and Cartesian Decompositions
Title | Permutation Groups and Cartesian Decompositions PDF eBook |
Author | Cheryl E. Praeger |
Publisher | London Mathematical Society Le |
Pages | 338 |
Release | 2018-05-03 |
Genre | Mathematics |
ISBN | 0521675065 |
Concise introduction to permutation groups, focusing on invariant cartesian decompositions and applications in algebra and combinatorics.
Groups St Andrews 2017 in Birmingham
Title | Groups St Andrews 2017 in Birmingham PDF eBook |
Author | C. M. Campbell |
Publisher | Cambridge University Press |
Pages | 510 |
Release | 2019-04-11 |
Genre | Mathematics |
ISBN | 110872874X |
These proceedings of 'Groups St Andrews 2017' provide a snapshot of the state-of-the-art in contemporary group theory.
New Directions in Locally Compact Groups
Title | New Directions in Locally Compact Groups PDF eBook |
Author | Pierre-Emmanuel Caprace |
Publisher | Cambridge University Press |
Pages | 367 |
Release | 2018-02-08 |
Genre | Mathematics |
ISBN | 1108349544 |
This collection of expository articles by a range of established experts and newer researchers provides an overview of the recent developments in the theory of locally compact groups. It includes introductory articles on totally disconnected locally compact groups, profinite groups, p-adic Lie groups and the metric geometry of locally compact groups. Concrete examples, including groups acting on trees and Neretin groups, are discussed in detail. An outline of the emerging structure theory of locally compact groups beyond the connected case is presented through three complementary approaches: Willis' theory of the scale function, global decompositions by means of subnormal series, and the local approach relying on the structure lattice. An introduction to lattices, invariant random subgroups and L2-invariants, and a brief account of the Burger–Mozes construction of simple lattices are also included. A final chapter collects various problems suggesting future research directions.
Partial Differential Equations in Fluid Mechanics
Title | Partial Differential Equations in Fluid Mechanics PDF eBook |
Author | Charles L. Fefferman |
Publisher | Cambridge University Press |
Pages | 339 |
Release | 2018-09-27 |
Genre | Mathematics |
ISBN | 1108573592 |
The Euler and Navier–Stokes equations are the fundamental mathematical models of fluid mechanics, and their study remains central in the modern theory of partial differential equations. This volume of articles, derived from the workshop 'PDEs in Fluid Mechanics' held at the University of Warwick in 2016, serves to consolidate, survey and further advance research in this area. It contains reviews of recent progress and classical results, as well as cutting-edge research articles. Topics include Onsager's conjecture for energy conservation in the Euler equations, weak-strong uniqueness in fluid models and several chapters address the Navier–Stokes equations directly; in particular, a retelling of Leray's formative 1934 paper in modern mathematical language. The book also covers more general PDE methods with applications in fluid mechanics and beyond. This collection will serve as a helpful overview of current research for graduate students new to the area and for more established researchers.