Document Type

Article

Publication Date

2006

Abstract

Given a finite connected graph G and specifications for a closed, connected pseudosurface, we characterize when G can be imbedded in a closed, connected pseudosurface with the given specifications. The specifications for the pseudosurface are: the number of face-connected components, the number of pinches, the number of crosscaps and handles, and the dimension of the first Z2-homology group. The characterizations are formulated in terms of the existence of a dual graph G ∗ on the same set of edges as G which satisfies algebraic conditions inspired by homology groups and their intersection products.

Repository Citation

Abrams, L., & Slilaty, D. (2006). Algebraic Characterizations of Graph Imbeddability in Surfaces and Pseudosurfaces. Journal of Knot Theory and Its Ramifications, 15, 681-693.
https://corescholar.libraries.wright.edu/math/321