In mathematics, simple homotopy theory is a homotopy theory (a branch of algebraic topology) that concerns with the simple-homotopy type of a space. It...

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...

of topology, a simple-homotopy equivalence is a refinement of the concept of homotopy equivalence. Two CW-complexes are simple-homotopy equivalent if they...

in homotopy theory and (higher) category theory, coherency is the standard that equalities or diagrams must satisfy when they hold "up to homotopy" or...

object of this category a simpler object that still retains sufficient information about the object of interest. Homotopy groups are such a way of associating...

point of view of simple homotopy theory" (PDF), Publications Mathématiques de l'IHÉS, 15: 5–93 Milnor, J (1970), "Algebraic K-theory and Quadratic Forms"...

logic and computer science, homotopy type theory (HoTT) refers to various lines of development of intuitionistic type theory, based on the interpretation...

Marian. New York: Springer. ISBN 9780387215976. OCLC 55897585. Cohen, Marshall M. (1973) A Course in Simple-Homotopy Theory, Springer-Verlag New York v t e...

Zermelo–Fraenkel set theory. This led to proposals such as Lawvere's Elementary Theory of the Category of Sets (ETCS). Homotopy type theory continues in this...

{\displaystyle 0<a<f(q),} then M a {\displaystyle M^{a}} is a disk, which is homotopy equivalent to a point (a 0-cell) which has been "attached" to the empty...

topology, rational homotopy theory is a simplified version of homotopy theory for topological spaces, in which all torsion in the homotopy groups is ignored...

was "symmetry". This opened up a new area of research, homotopy type theory, where category theory was applied to the identity type. Russell's (1902) Letter...

In mathematics, especially homotopy theory, the homotopy fiber (sometimes called the mapping fiber) is part of a construction that associates a fibration...

the obstruction to a homotopy equivalence f : X → Y {\displaystyle f\colon X\to Y} of finite CW-complexes being a simple homotopy equivalence is its Whitehead...

was initially introduced by J. H. C. Whitehead to meet the needs of homotopy theory. CW complexes have better categorical properties than simplicial complexes...

MR 0212840 Hatcher, A.E. (1978). "Concordance spaces, higher simple-homotopy theory, and applications". Algebraic and geometric topology (Proc. Sympos...

In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, does not change under local...

univalent foundations and related to it homotopy type theory. Within homotopy type theory, a set may be regarded as a homotopy 0-type, with universal properties...

is the first and simplest homotopy group. The fundamental group is a homotopy invariant—topological spaces that are homotopy equivalent (or the stronger...

ISSN 0003-486X, JSTOR 1970299 Marshall M. Cohen (1973), "A Course in Simple-Homotopy Theory", Graduate Texts in Mathematics, Graduate Texts in Mathematics,...

In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ('arrows') called 'weak equivalences'...

distinguishing spaces that are homotopy equivalent but not homeomorphic. This was the origin of simple homotopy theory. The use of the term geometric...

"Henry", was a British mathematician and was one of the founders of homotopy theory. He was born in Chennai (then known as Madras), in India, and died...

construct a homotopy on a differential system in general form. The convergence-control parameter is a non-physical variable that provides a simple way to verify...

Texts in Mathematics 139, 1993. Cohen, Marshall M., A Course in Simple-Homotopy Theory, Springer Graduate Texts in Mathematics 10, 1973. Brody, E. J. (1960)...

In theoretical computer science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation...

effects on the homology, homotopy groups, or other invariants of the manifold are known. A relatively easy argument using Morse theory shows that a manifold...

perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem....

higher group, or simple space, with trivial π 1 {\displaystyle \pi _{1}} such that a group G {\displaystyle G} acts on it homotopy theoretically. This...

In the mathematical field of algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other....