Publication

Une dégustation topologique: homotopy theory in the Swiss Alps : Proceedings of the Arolla conference on algebraic topology, Arolla, Switzerland, August 25-September 1, 1999.

2000
Conference Proceedings

Abstract

The talks given at the Arolla Conference on Algebraic Topology covered a broad spectrum of current research in homotopy theory, offering participants the possibility to sample and relish selected morsels of homotopy theory, much as a participant in a wine tasting partakes of a variety of fine wines. True to the spirit of the conference, the proceedings included in this volume present a savory sampler of homotopical delicacies. Readers will find within these pages a compilation of articles describing current research in the area, including classical stable and unstable homotopy theory, configuration spaces, group cohomology, K-theory, localization, p-compact groups, and simplicial theory.

Official source

https://infoscience.epfl.ch/entities/publication/850d1fee-79fc-45dc-94d9-d81ca7de5dd0

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2000
Conference Proceedings

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/850d1fee-79fc-45dc-94d9-d81ca7de5dd0

About this result

Related concepts (32)

A¹ homotopy theory

In algebraic geometry and algebraic topology, branches of mathematics, A1 homotopy theory or motivic homotopy theory is a way to apply the techniques of algebraic topology, specifically homotopy, to algebraic varieties and, more generally, to schemes. The theory is due to Fabien Morel and Vladimir Voevodsky. The underlying idea is that it should be possible to develop a purely algebraic approach to homotopy theory by replacing the unit interval [0, 1], which is not an algebraic variety, with the affine line A1, which is.

Stable homotopy theory

In mathematics, stable homotopy theory is the part of homotopy theory (and thus algebraic topology) concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor. A founding result was the Freudenthal suspension theorem, which states that given any pointed space , the homotopy groups stabilize for sufficiently large. In particular, the homotopy groups of spheres stabilize for . For example, In the two examples above all the maps between homotopy groups are applications of the suspension functor.

Homotopy theory

In mathematics, homotopy theory is a systematic study of situations in which maps can come with homotopies between them. It originated as a topic in algebraic topology but nowadays is studied as an independent discipline. Besides algebraic topology, the theory has also been used in other areas of mathematics such as algebraic geometry (e.g., A1 homotopy theory) and (specifically the study of ). In homotopy theory and algebraic topology, the word "space" denotes a topological space.

Related publications (1)

Une dégustation topologique: homotopy theory in the Swiss Alps : Proceedings of the Arolla conference on algebraic topology, Arolla, Switzerland, August 25-September 1, 1999.

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