This article includes a list of general references, but it lacks sufficient corresponding inline citations. Please help to improve this article by introducing more precise citations. (September 2022) (Learn how and when to remove this template message) Illustration of how a 2-sphere can be wrapped twice around another 2-sphere. Edges should be identified. In the mathematical field of algebraic top
The Hopf fibration can be visualized using a stereographic projection of S3 to R3 and then compressing R3 to a ball. This image shows points on S2 and their corresponding fibers with the same color. Pairwise linked keyrings mimic part of the Hopf fibration. In the mathematical field of differential topology, the Hopf fibration (also known as the Hopf bundle or Hopf map) describes a 3-sphere (a hyp
In homological algebra and algebraic topology, a spectral sequence is a means of computing homology groups by taking successive approximations. Spectral sequences are a generalization of exact sequences, and since their introduction by Jean Leray (1946a, 1946b), they have become important computational tools, particularly in algebraic topology, algebraic geometry and homological algebra. Discovery
Intuitively, a covering locally projects a "stack of pancakes" above an open neighborhood onto In topology, a covering or covering projection is a map between topological spaces that, intuitively, locally acts like a projection of multiple copies of a space onto itself. In particular, coverings are special types of local homeomorphisms. If is a covering, is said to be a covering space or cover of
In differential topology, the transversality theorem, also known as the Thom transversality theorem after French mathematician René Thom, is a major result that describes the transverse intersection properties of a smooth family of smooth maps. It says that transversality is a generic property: any smooth map , may be deformed by an arbitrary small amount into a map that is transverse to a given s
"Gauss–Bonnet" redirects here. Not to be confused with Gauss–Bonnet gravity. This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Gauss–Bonnet theorem" – news · newspapers · books · scholar · JSTOR (October 2020) (Learn how and when to remove this message)
A Penrose triangle depicts a nontrivial element of the first cohomology of an annulus with values in the group of distances from the observer[1] In mathematics, specifically algebraic topology, Čech cohomology is a cohomology theory based on the intersection properties of open covers of a topological space. It is named for the mathematician Eduard Čech. Motivation[edit] Let X be a topological spac
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