New Spaces in Mathematics: Volume 1: Formal and Conceptual Reflections

ISBN-13: 9781108490634 / Angielski / Twarda / 2021 / 550 str.

Mathieu Anel; Gabriel Catren

Opis

In this graduate-level book, leading researchers explore various new notions of 'space' in mathematics.

Recenzje

'The essays are self-contained, providing motivation to read selectively. Examples in each chapter illustrate the usefulness of these new notions of space … Recommended.' M. Clay, Choice Magazine

Spis treści

Introduction Mathieu Anel and Gabriel Catren; Part I. Differential geometry: 1. An Introduction to diffeology Patrick Iglesias-Zemmour; 2. New methods for old spaces: synthetic differential geometry Anders Kock; 3. Microlocal analysis and beyond Pierre Schapira; Part II. Topology and algebraic topology: 4. Topo-logie Mathieu Anel and André Joyal; 5. Spaces as infinity-groupoids Timothy Porter; 6. Homotopy type theory: the logic of space Michael Shulman; Part III. Algebraic geometry: 7. Sheaves and functors of points Michel Vaquié; 8. Stacks Nicole Mestrano and Carlos Simpson; 9. The geometry of ambiguity: an introduction to the ideas of derived geometry Mathieu Anel; 10. Geometry in dg categories Maxim Kontsevich.