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 impetus of the proposal is the recent breakthrough in which, inspired by rational homotopy theory, we introduced koszul modules as novel homological objects establishing striking connections between algebraic geometry and geometric group theory.
The proceedings of a July 2017 conference on homotopy theory held in Urbana, Illinois contains 11 selected papers.
James, Fibrewise homotopy theory. Springer, Berlin, 1998.
He says only a few things about this in the book, explaining on the book's companion website, https://mathematicswithoutapologies.wordpress.com/, that he is not well versed in homotopy theory. But he does entertain the possibility (pp.
Arone, A note on the homology of [[SIGMA].sub.n], the Schwartz genus, and solving polynomial equations, in An alpine anthology of homotopy theory, Contemp.
"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.
Bergner, "Three models for the homotopy theory of homotopy theories," Topology, vol.
Hilton, An Introduction to Homotopy Theory, Cambridge University Press, Cambridge, UK, 1953.
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.sub.0]) of graphs.
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.