homology group
61Covering groups of the alternating and symmetric groups — In the mathematical area of group theory, the covering groups of the alternating and symmetric groups are groups that are used to understand the projective representations of the alternating and symmetric groups. The covering groups were… …
62Morse theory — Morse function redirects here. In another context, a Morse function can also mean an anharmonic oscillator: see Morse potential In differential topology, the techniques of Morse theory give a very direct way of analyzing the topology of a… …
63Torus — Not to be confused with Taurus (disambiguation). This article is about the surface and mathematical concept of a torus. For other uses, see Torus (disambiguation). A torus As the distance to th …
64Induced homomorphism (algebraic topology) — In mathematics, especially in the area of topology known as algebraic topology, an induced homomorphism is a way of relating the algebraic invariants of topological spaces which are already related by a continuous function. Such homomorphism… …
65Betti number — In algebraic topology, the Betti number of a topological space is, in intuitive terms, a way of counting the maximum number of cuts that can be made without dividing the space into two pieces. This defines, in fact, what is called the first Betti …
66Ring (mathematics) — This article is about algebraic structures. For geometric rings, see Annulus (mathematics). For the set theory concept, see Ring of sets. Polynomials, represented here by curves, form a ring under addition and multiplication. In mathematics, a… …
67Emmy Noether — Amalie Emmy Noether Born 23 March 1882(1882 03 23) …
68Massey product — The Massey product is an algebraic generalization of the phenomenon of Borromean rings. In algebraic topology, the Massey product is a cohomology operation of higher order introduced in (Massey 1958), which generalizes the cup product …
69Rokhlin's theorem — In 4 dimensional topology, a branch of mathematics, Rokhlin s theorem states that if a smooth, compact 4 manifold M has a spin structure (or, equivalently, the second Stiefel Whitney class w 2( M ) vanishes), then the signature of its… …
70Künneth theorem — In mathematics, especially in homological algebra and algebraic topology, a Künneth theorem is a statement relating the homology of two objects to the homology of their product. The classical statement of the Künneth theorem relates the singular… …
