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When can homology classes be realized as the image of fundamental classes of manifolds? The answer is known, and singular bordism groups provide insight into this problem.

The Stiefel-Whitney number is defined in terms of the Stiefel-Whitney class of a manifold as follows. For any collection of Stiefel-Whitney classes such that their cup ...

A map phi:M->M where M is a manifold is C^r structurally stable if any C^r perturbation is topologically conjugate to phi. Here, C^r perturbation means a function psi such ...

A set in a Polish space is a Borel set iff it is both analytic and coanalytic. For subsets of w, a set is delta_1^1 iff it is "hyperarithmetic."

The space join of a topological space X and a pair of points S^0, Sigma(X)=X*S^0.

A topological basis is a subset B of a set T in which all other open sets can be written as unions or finite intersections of B. For the real numbers, the set of all open ...

The topological entropy of a map M is defined as h_T(M)=sup_({W_i})h(M,{W_i}), where {W_i} is a partition of a bounded region W containing a probability measure which is ...

Two maps phi,psi:M->M are said to be topologically conjugate if there exists a homeomorphism h:M->M such that phi degreesh=h degreespsi, i.e., h maps psi-orbits onto ...

A tubular neighborhood of a submanifold N in M is an embedding of the normal bundle (nu_N) of N into M, i.e., f:nu_N->M, where the image of the zero section of the normal ...

The space |K| which is the subset of R^n that is the union of the simplices in a simplicial complex K. The term polytope is sometimes used as a synonym for underlying space ...