homotopy theory

homotopy theory

[hō′mäd·ə·pē ‚thē·ə·rē]
(mathematics)
The study of the topological structure of a space by examining the algebraic properties of its various homotopy groups.
References in periodicals archive ?
the study of moduli spaces of manifolds via homotopy theory has seen a great deal of development in the last 20 years, The breakthrough result being madsen and weiss~ calculation of the stable homology of moduli spaces of surfaces.
Each paper discusses a different subfield of algebraic geometry that has seen significant progress in the past 10 years, such as birational geometry of moduli spaces of sheaves, Gromov-Witten theory, degenerations of Hodge structure, and unstable motivic homotopy theory.
com/, that he is not well versed in homotopy theory.
n], the Schwartz genus, and solving polynomial equations, in An alpine anthology of homotopy theory, Contemp.
Throughout this paper we will often use rational homotopy theory techniques for which much more than needed can be found in [6].
An Illustrated Introduction to Topology and Homotopy" by academician and mathematician Sasho Kalajdzievski (University of Manitoba, Winnipeg, Canada) is a 485 page textbook that has as its specific focus topology and homotopy theory and applications.
One of the main property of any consistent homotopy theory is the existence of a long exact sequence associated to any based pair (G, H, [v.
of Western Michigan) develops classical homotopy theory and some important developments that flow from it using the modern techniques of homotopy limits and co-limits.
Hom complexes and homotopy theory in the category of graphs.
Homotopy theory of function spaces and related topics; proceedings.
AM95] Marc Aubry, Homotopy Theory and Models, DMV Seminar B.
The main result in this paper was announced during the Cech centennial homotopy theory conference at Northeastern University in June 1993.