Mapping schemes realizable by obstructed topological polynomials

Polynomials in Topological Fields

Evaluations of Topological Tutte Polynomials

We find a number of new combinatorial identities for, and interpretations of evaluations of, the topological Tutte polynomials of Las Vergnas, L(G), and of and Bollobás and Riordan, R(G), as well as for the classical Tutte polynomial T (G). For example, we express R(G) and T (G) as a sum of chromatic polynomials, show that R(G) counts non-crossing graph states and k-valuations, and reformulate ...

Thurston Equivalence of Topological Polynomials

We answer Hubbard’s question on determining the Thurston equivalence class of “twisted rabbits”, i.e. composita of the “rabbit” polynomial with nth powers of the Dehn twists about its ears. The answer is expressed in terms of the 4-adic expansion of n. We also answer the equivalent question for the other two families of degree-2 topological polynomials with three post-critical points. In the pr...

Topological Equivalence of Complex Polynomials

The following numerical control over the topological equivalence is proved: two complex polynomials in n 6= 3 variables and with isolated singularities are topologically equivalent if one deforms into the other by a continuous family of polynomial functions fs : C → C with isolated singularities such that the degree, the number of vanishing cycles and the number of atypical values are constant ...

DNA Mapping Algorithms: Topological Mapping

There are several basic approaches that can be used in attempting to produce high-resolution DNA restriction maps. A standard approach is the match/merge approach in which first the topology of the map units being mapped together is suppressed and lists of potential matches between fragments are generated, and second the topology is introduced to eliminate matchlists which are inconsistent with...