Real Homotopy of Configuration Spaces

Real Homotopy of Configuration Spaces

Author: Najib Idrissi

Publisher: Springer Nature

Published: 2022-06-11

Total Pages: 201

ISBN-13: 3031044282

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This volume provides a unified and accessible account of recent developments regarding the real homotopy type of configuration spaces of manifolds. Configuration spaces consist of collections of pairwise distinct points in a given manifold, the study of which is a classical topic in algebraic topology. One of this theory’s most important questions concerns homotopy invariance: if a manifold can be continuously deformed into another one, then can the configuration spaces of the first manifold be continuously deformed into the configuration spaces of the second? This conjecture remains open for simply connected closed manifolds. Here, it is proved in characteristic zero (i.e. restricted to algebrotopological invariants with real coefficients), using ideas from the theory of operads. A generalization to manifolds with boundary is then considered. Based on the work of Campos, Ducoulombier, Lambrechts, Willwacher, and the author, the book covers a vast array of topics, including rational homotopy theory, compactifications, PA forms, propagators, Kontsevich integrals, and graph complexes, and will be of interest to a wide audience.


Geometry and Topology of Configuration Spaces

Geometry and Topology of Configuration Spaces

Author: Edward R. Fadell

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 314

ISBN-13: 3642564461

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With applications in mind, this self-contained monograph provides a coherent and thorough treatment of the configuration spaces of Euclidean spaces and spheres, making the subject accessible to researchers and graduates with a minimal background in classical homotopy theory and algebraic topology.


Cohomological Methods in Homotopy Theory

Cohomological Methods in Homotopy Theory

Author: Jaume Aguade

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 413

ISBN-13: 3034883129

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This book contains a collection of articles summarizing the state of knowledge in a large portion of modern homotopy theory. A call for articles was made on the occasion of an emphasis semester organized by the Centre de Recerca Matemtica in Bellaterra (Barcelona) in 1998. The main topics treated in the book include abstract features of stable and unstable homotopy, homotopical localizations, p-compact groups, H-spaces, classifying spaces for proper actions, cohomology of discrete groups, K-theory and other generalized cohomology theories, configuration spaces, and Lusternik-Schnirelmann category. The book is addressed to all mathematicians interested in homotopy theory and in geometric aspects of group theory. New research directions in topology are highlighted. Moreover, this informative and educational book serves as a welcome reference for many new results and recent methods.


Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)

Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)

Author: Boyan Sirakov

Publisher: World Scientific

Published: 2019-02-27

Total Pages: 5393

ISBN-13: 9813272899

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The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.


Configuration Spaces

Configuration Spaces

Author: Filippo Callegaro

Publisher: Springer

Published: 2016-08-27

Total Pages: 385

ISBN-13: 3319315803

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This book collects the scientific contributions of a group of leading experts who took part in the INdAM Meeting held in Cortona in September 2014. With combinatorial techniques as the central theme, it focuses on recent developments in configuration spaces from various perspectives. It also discusses their applications in areas ranging from representation theory, toric geometry and geometric group theory to applied algebraic topology.


Cubical Homotopy Theory

Cubical Homotopy Theory

Author: Brian A. Munson

Publisher: Cambridge University Press

Published: 2015-10-06

Total Pages: 649

ISBN-13: 1107030250

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


Handbook of Homotopy Theory

Handbook of Homotopy Theory

Author: Haynes Miller

Publisher: CRC Press

Published: 2020-01-23

Total Pages: 982

ISBN-13: 1351251619

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The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.


Developments in Mathematics

Developments in Mathematics

Author: V Arnold

Publisher: CRC Press

Published: 1993-01-01

Total Pages: 312

ISBN-13: 9780412452703

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A collection of seven survey articles especially commissioned by Professors Arnold and Monastyrsky highlighting areas where the Moscow scholl has amde significant recent contributions to theoretical mathematics. Contributions include papers on Knot theory, supersurfaces and dynamical systems. This book contains articles on aspects of mathematics that have become increasingly important in the west. The editors are internationally renowned for the standard of their work.