homology group
101Simplicial approximation theorem — In mathematics, the simplicial approximation theorem is a foundational result for algebraic topology, guaranteeing that continuous mappings can be (by a slight deformation) approximated by ones that are piecewise of the simplest kind. It applies… …
102Circuit rank — The circuit rank of a graph G (also known as the cyclomatic number of G) is the minimum number r of edges to remove from the graph to make it cycle free. It has the formula r = m − n + c, where m is the number |E(G)| of edges in G, n is the… …
103Lefschetz hyperplane theorem — In mathematics, the Lefschetz hyperplane theorem states that a hyperplane section W of a non singular complex algebraic variety V , in complex projective space, inherits most of its algebraic topology from V . This allows certain geometrical… …
104SUMO protein — Small Ubiquitin like Modifier or SUMO proteins are a family of small proteins that are covalently attached to and detached from other proteins in cells to modify their function. SUMOylation is a post translational modification involved in various …
105Kervaire invariant — In mathematics, the Kervaire invariant, named for Michel Kervaire, is defined in geometric topology. It is an invariant of 4 n + 2 dimensional almost parallelizable smooth manifolds M , taking values in the 2 element group :Z/2Z. It is equal to… …
106Ε-quadratic form — In mathematics, specifically the theory of quadratic forms, an ε quadratic form is a generalization of quadratic forms to skew symmetric settings and to * rings; epsilon = pm 1, accordingly for symmetric or skew symmetric. They are also called (… …
107Conservative vector field — In vector calculus a conservative vector field is a vector field which is the gradient of a function, known in this context as a scalar potential. Conservative vector fields have the property that the line integral from one point to another is… …
108Signature of a knot — The signature of a knot is a topological invariant in knot theory. It may be computed from the Seifert surface.Given a knot K in the 3 sphere, it has a Seifert surface S whose boundary is K . The Seifert form of S is the pairing phi : H 1(S) imes …
109Dold–Thom theorem — In algebraic topology, the Dold–Thom theorem, proved by Albrecht Dold and Thom (1956, 1958), states that the homotopy group πi(SP(X)) of the infinite symmetric product SP(X) of X is the i th singular reduced homology group of X , usually… …
110Simplicial complex — In mathematics, a simplicial complex is a topological space of a particular kind, constructed by gluing together points, line segments, triangles, and their n dimensional counterparts (see illustration). Simplicial complexes should not be… …
