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Let K be a finite complex, and let phi:C_p(K)->C_p(K) be a chain map, then sum_(p)(-1)^pTr(phi,C_p(K))=sum_(p)(-1)^pTr(phi_*,H_p(K)/T_p(K)).

A list of problems in low-dimensional topology maintained by Kirby (1995). The list currently runs about 380 pages.

A space X is locally pathwise-connected if for every neighborhood around every point in X, there is a smaller, pathwise-connected neighborhood.

Let G be a locally compact Abelian group. Let G^* be the group of all continuous homeomorphisms G->R/Z, in the compact open topology. Then G^* is also a locally compact ...

A Reeb component is a Reeb foliation (M,F) whose leaves are proper. A foliation which has no Reeb components is said to be Reebless.

A foliation which has no Reeb components is said to be Reebless.

The set St^_v-Stv, where St^_v is a closed star and Stv is a star, is called the link of v in a simplicial complex K and is denoted Lkv (Munkres 1993, p. 11).

A subspace A of X is called a strong deformation retract of X if there is a homotopy F:X×I->X (called a retract) such that for all x in X, a in A, and t in I, 1. F(x,0)=x, 2. ...

The term cube is used in topology to denote the Cartesian product of any (finite or infinite) number of copies of the closed interval [0,1] equipped with the product topology ...

If K is a simplicial complex, let V be the vertex set of K. Furthermore, let K be the collection of all subsets {a_0,...,a_n} of V such that the vertices a_0, ..., a_n span a ...