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The branch of algebraic topology which deals with homotopy groups. Homotopy methods can be used to solve systems of polynomials by embedding the polynomials in a family of ...

If K is a finite complex and h:|K|->|K| is a continuous map, then Lambda(h)=sum(-1)^pTr(h_*,H_p(K)/T_p(K)) is the Lefschetz number of the map h.

A simplicial complex K is said to be locally finite if each vertex of K belongs only to finitely many simplices of K.

Obstruction theory studies the extensibility of maps using algebraic gadgets. While the terminology rapidly becomes technical and convoluted (as Iyanaga and Kawada (1980) ...

The ith Pontryagin class of a vector bundle is (-1)^i times the ith Chern class of the complexification of the vector bundle. It is also in the 4ith cohomology group of the ...

Let f:K^((0))->L^((0)) be a bijective correspondence such that the vertices v_0, ..., v_n of K span a simplex of K iff f(v_0), ..., f(v_n) span a simplex of L. Then the ...

Let K and L be simplicial complexes, and let f:K^((0))->L^((0)) be a map. Suppose that whenever the vertices v_0, ..., v_n of K span a simplex of K, the points f(v_0), ..., ...

If L is a subcollection of a simplicial complex K that contains all faces of its elements, then L is another simplicial complex called a simplicial subcomplex.

The space of immersions of a manifold in another manifold is homotopically equivalent to the space of bundle injections from the tangent space of the first to the tangent ...

Any link can be represented by a closed braid.