homotopy group
71Serre spectral sequence — In mathematics, the Serre spectral sequence (sometimes Leray Serre spectral sequence to acknowledge earlier work of Jean Leray) is a basic tool of algebraic topology. It expresses the singular (co)homology of the total space E of a (Serre)… …
72Magnetic monopole — It is impossible to make magnetic monopoles from a bar magnet. If a bar magnet is cut in half, it is not the case that one half has the north pole and the other half has the south pole. Inst …
73Contractible space — In mathematics, a topological space X is contractible if the identity map on X is null homotopic, i.e. if it is homotopic to some constant map.[1][2] Intuitively, a contractible space is one that can be continuously shrunk to a point. A… …
74Steenrod algebra — In algebraic topology, a branch of mathematics, the Steenrod algebra is a structure occurring in the theory of cohomology operations. It is an object of great importance, most especially to homotopy theorists. More precisely, for a given prime… …
75Kan fibration — The notion of a Kan fibration is a part of the theory of simplicial sets in mathematics. Kan fibrations are the fibrations in the model category theoretic sense on the category of simplicial sets and are therefore of fundamental importance. The… …
76Orientability — For orientation of vector spaces, see orientation (mathematics). For other uses, see Orientation (disambiguation). The torus is an orientable surface …
77Weak equivalence — In mathematics, a weak equivalence is a notion from homotopy theory which in some sense identifies objects that have the same basic shape . This notion is formalized in the axiomatic definition of a closed model category.Formal definitionA closed …
78Acyclic space — In mathematics, an acyclic space is a topological space X in which cycles are always boundaries, in the sense of homology theory. This implies that the integral homology groups in all dimensions of X are isomorphic to the corresponding homology… …
79Hopf fibration — In the mathematical field of topology, the Hopf fibration (also known as the Hopf bundle or Hopf map) describes a 3 sphere (a hypersphere in four dimensional space) in terms of circles and an ordinary sphere. Discovered by Heinz Hopf in 1931, it… …
80Wess-Zumino-Witten model — In theoretical physics and mathematics, the Wess Zumino Witten (WZW) model, also called the Wess Zumino Novikov Witten model, is a simple model of conformal field theory whose solutions are realized by affine Kac Moody algebras. It is named after …
