homotopy

homotopy hypothesis-theorem delooping hypothesis-theorem stabilization hypothesis-theorem The generalization of the bicategory Span to (∞,n)-categories: An -category of correspondences in ∞-groupoid is an (∞,n)-category whose objects are ∞-groupoids; morphisms are correspondences in ∞Grpd 2-morphisms are correspondences of correspondences (where the triangular sub-diagrams are filled with 2-morph…

Michael Hopkins: The mathematical work of Douglas C. Ravenel, Homology Homotopy Appl. 10 3 (2008) 1-13 [euclid:hha/1251832464] On the Adams-Novikov spectral sequence: On chromatic homotopy theory and introducing Ravenel's spectra and Ravenel's conjectures: On stable homotopy groups of spheres and chromatic homotopy theory: On stable homotopy groups of spheres and chromatic homotopy theory: Doug R…

Thomas J. Lada On homology of iterated loop spaces and the Dyer-Lashof operations?: On -algebras: Tom Lada, Jim Stasheff: Introduction to sh Lie algebras for physicists, Int. J. Theo. Phys. 32 (1993) 1087–1103 [doi:10.1007/BF00671791, arXiv:hep-th/9209099] Tom Lada, Martin Markl: Strongly homotopy Lie algebras, Communications in Algebra 23 6 (1995) [doi:10.1080/00927879508825335, arXiv:hep-th/940…

Let $G$ be a finite group. Elmendorf's theorem compares two approaches to the homotopy theory of $G$-spaces. I'll follow this generalization by Stephan [1] in a (nice) model category $C$. Presheaves ...

homotopy theory, (∞,1)-category theory, homotopy type theory flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed… models: topological, simplicial, localic, … see also algebraic topology Introductions Definitions Paths and cylinders Homotopy groups Basic facts Theorems The localization of a space (really: homotopy type, ∞-groupoid) or spectrum with respect to some…

Computing for is easy. By definition, , and by cellular approximation, we note that every map can be homotoped to a cellular map. It is obvious that all such cellular maps are trivial, so that if . The homotopy groups are more interesting, and can be computed via the Hurewicz theorem: Theorem (Hurewicz): There is […]