Embedding simplicial arcs into the plane
by
Piotr Minc
Auburn University

Suppose G₀ @ < f₀ << G₁ @ < f₁ << G₂ @ < f₂ << ¼ is an inverse system of graphs. Place each G_i into the plane with an embedding h_i so that h_i+1 is sufficiently close to h_i °f_i. It is wery well known that the limit of { h_i(G_i) } in the plane is homeomorphic to the inverse limit of the system. Motivated by this technique, we will study the combinatorics of the following problem. Suppose j: G₁ ® G₀ is a simplicial map between graphs and an embedding h₀ of G₀ into the plane. Under what conditions can G₁ be embedded into the plane with an embedding sufficiently close to h₀ °j ? We will answer this question in the case when G₁ is an arc.

Date received: June 27, 1997

Copyright © 1997 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caao-33.