International Congress of Mathematicians: Topology

ICM 2018 - Rio

Topology

Topology

Geometry, Topology, and Dynamics in Negative Curvature

Aperiodic Order

Aperiodic Order

Volume 1: A Mathematical Invitation Michael Baake and Uwe Grimm

Volume 2: Crystallography and Almost Periodicity Edited by Michael Baake and Uwe Grimm

A comprehensive introductory monograph on the theory of aperiodic order, with numerous illustrations and examples.

The second volume in a series exploring the mathematics of aperiodic order. Covers various aspects of crystallography.

Encyclopedia of Mathematics and its Applications, 149

Encyclopedia of Mathematics and its Applications, 166

August 2013 234 x 156 mm 552pp 145 b/w illus. 18 colour illus. 10 tables 978-0-521-86991-1 Hardback £79.99 / US$125.00 C

November 2017 234 x 156 mm 404pp 52 b/w illus.

978-0-521-86992-8 Hardback £110.00 / US$140.00 C

Synthetic Differential Topology

Higher Categories and Homotopical Algebra

Marta Bunge, Felipe Gago and Ana María San Luis

Denis-Charles Cisinski

Factorization Algebras in Quantum Field Theory

Edited by C. S. Aravinda F. T. Farrell and J.-F. Lafont

Ten high-quality survey articles provide an overview of important recent developments in the mathematics surrounding negative curvature.

London Mathematical Society Lecture Note Series, 425 January 2016 228 x 152 mm 381pp 25 b/w illus.

978-1-107-52900-7 Paperback £60.99 / US$85.99 C

Represents the state of the art in the new field of synthetic differential topology.

London Mathematical Society Lecture Note Series, 448 March 2018 228 x 152 mm 232pp 23 b/w illus.

978-1-108-44723-2 Paperback £50.00 / US$80.00 C

Cambridge Studies in Advanced Mathematics December 2019 978-1-108-47320-0 Hardback TBA / TBA

Volume 1 Kevin Costello and Owen Gwilliam

This first volume develops factorization algebras with a focus upon examples exhibiting their use in field theory, which will be useful for researchers and graduates.

New Mathematical Monographs, 31

The Homotopy Theory of (∞,1)-Categories Julia E. Bergner

An introductory treatment to the homotopy theory of homotopical categories, presenting several models and comparisons between them.

London Mathematical Society Student Texts, 90 March 2018 228 x 152 mm 284pp 978-1-107-49902-7 Paperback £29.99 / US$39.99 P

Floer Homology Groups in Yang-Mills Theory S. K. Donaldson Assisted by M. Furuta and D. Kotschick

Fields-medal winner Donaldson reviews current work, including his own, on the theory of Floer.

Cambridge Tracts in Mathematics, 147 January 2002 228 x 152 mm 246pp 978-0-521-80803-3 Hardback £99.99 / US$160.00 C

December 2016 228 x 152 mm 398pp 978-1-107-16310-2 Hardback £110.00 / US$150.00 C

20% discount online at www.cambridge.org/ICM2018

Topology

Automorphisms and Equivalence Relations in Topological Dynamics David B. Ellis and Robert Ellis

A lucid and self-contained treatment of many key ideas in topological dynamics, achieved by focusing on equivalence relations and automorphisms.

London Mathematical Society Lecture Note Series, 412

Topology of Stratified Spaces

Algebraic Topology

Edited by Greg Friedman Eugénie Hunsicker Anatoly Libgober and Laurentiu Maxim

Allen Hatcher

This book explores the study of singular spaces using techniques from areas within geometry and topology and the interactions among them.

October 2014 234 x 156 mm 490pp 978-1-107-45947-2 Paperback £50.00 / US$74.99 C

An introductory textbook suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises.

February 2002 253 x 177 mm 556pp 978-0-521-79540-1 Paperback £29.99 / US$49.99 X

Hyperbolic Manifolds

Peter Kronheimer and Tomasz Mrowka

An Introduction in 2 and 3 Dimensions Albert Marden

A comprehensive treatment of Floer homology, based on the Seiberg–Witten equations, first published in 2007.

New Mathematical Monographs, 10 November 2010 228 x 152 mm 808pp 12 b/w illus.

978-0-521-18476-2 Paperback £57.99 / US$92.99 C

This study of hyperbolic geometry has both pedagogy and research in mind, and includes exercises and further reading for each chapter.

February 2016 247 x 174 mm 529pp 55 b/w illus. 21 colour illus. 250 exercises 978-1-107-11674-0 Hardback £51.99 / US$79.99 P

Edited by Peter H. Kropholler Ian J. Leary, Conchita Martínez-Pérez and Brita E. A. Nucinkis

Surveys the state of the art in geometric and cohomological group theory. Ideal entry point for young researchers.

London Mathematical Society Lecture Note Series, 444 October 2017 228 x 152 mm 276pp 50 b/w illus.

978-1-316-62322-0 Paperback £55.00 / US$70.00 C

June 2014 228 x 152 mm 281pp 80 exercises 978-1-107-63322-3 Paperback £47.99 / US$72.99 C

Monopoles and Three-Manifolds

Geometric and Cohomological Group Theory

Advances in Two-Dimensional Homotopy and Combinatorial Group Theory Edited by Wolfgang Metzler and Stephan Rosebrock

Presents the current state of knowledge in all aspects of two-dimensional homotopy theory. Useful for both students and experts.

London Mathematical Society Lecture Note Series, 446

Cubical Homotopy Theory Brian A. Munson and Ismar Volic

A modern, example-driven introduction to cubical diagrams and related topics such as homotopy limits and cosimplicial spaces.

New Mathematical Monographs, 25 October 2015 228 x 152 mm 644pp 20 b/w illus.

978-1-107-03025-1 Hardback £83.99 / US$125.00 P

November 2017 228 x 152 mm 290pp 50 b/w illus.

978-1-316-60090-0 Paperback £50.00 / US$65.00 C

20% discount online at www.cambridge.org/ICM2018

Topology

Symplectic Topology and Floer Homology

Symplectic Topology and Floer Homology

Categorical Homotopy Theory

Volume 1: Symplectic Geometry and Pseudoholomorphic Curves Yong-Geun Oh

Volume 2: Floer Homology and its Applications Yong-Geun Oh

Emily Riehl

The first part of a two-volume set offering a systematic explanation of symplectic topology. This volume covers the basic materials of Hamiltonian dynamics and symplectic geometry.

The second part of a two-volume set offering a systematic explanation of symplectic topology. This volume provides a comprehensive introduction to Hamiltonian and Lagrangian Floer theory.

New Mathematical Monographs, 28

New Mathematical Monographs, 29

September 2015 228 x 152 mm 420pp 35 b/w illus. 50 exercises 978-1-107-07245-9 Hardback £97.99 / US$150.00 C

September 2015 228 x 152 mm 472pp 10 b/w illus. 50 exercises 978-1-107-10967-4 Hardback £97.99 / US$150.00 C

This categorical perspective on homotopy theory helps consolidate and simplify one’s understanding of derived functors, homotopy limits and colimits, and model categories, among others.

New Mathematical Monographs, 24 August 2014 228 x 152 mm 372pp 55 exercises 978-1-107-04845-4 Hardback £70.00 / US$99.99 C

Polynomials and the mod 2 Steenrod Algebra Volume 1: The Peterson Hit Problem Grant Walker and Reginald M. W. Wood

The first of two volumes covering the Steenrod algebra and its various applications. Suitable as a graduate text.

London Mathematical Society Lecture Note Series, 441 November 2017 228 x 152 mm 370pp 978-1-108-41448-7 Paperback £60.00 / US$99.00 C

Polynomials and the mod 2 Steenrod Algebra

Differential Topology

Global Homotopy Theory

C. T. C. Wall

Stefan Schwede

Volume 2: Representations of GL (n,F2) Grant Walker and Reginald M. W. Wood

A comprehensive account giving advanced students and researchers an accessible route into the wide-ranging field of differential topology.

A comprehensive, self-contained approach to global equivariant homotopy theory, with many detailed examples and sample calculations.

Bjørn Ian Dundas

Cambridge Studies in Advanced Mathematics, 156

New Mathematical Monographs, 34

Cambridge Mathematical Textbooks

The second of two volumes covering the Steenrod algebra and its various applications. Ideal for researchers in pure mathematics.

London Mathematical Society Lecture Note Series, 442 November 2017 228 x 152 mm 378pp 1 b/w illus.

978-1-108-41445-6 Paperback £60.00 / US$99.00 C

July 2016 228 x 152 mm 353pp 30 b/w illus.

978-1-107-15352-3 Hardback £52.99 / US$77.99 P

September 2018 228 x 152 mm c.846pp 978-1-108-42581-0 Hardback £140.00 / US$195.00 C

A Short Course in Differential Topology Concise and modern introduction to differential topology with a hands-on approach and plentiful examples and exercises.

June 2018 253 x 177 mm 262pp 95 b/w illus. 230 exercises 978-1-108-42579-7 Hardback £39.99 / US$54.99 P

20% discount online at www.cambridge.org/ICM2018