We demonstrate that the proper homotopy equivalence relation for locally finite graphs is Borel complete. Furthermore, among the infinite graphs, there is a comeager equivalence class. As corollaries, we obtain the analogous results for the homeomorphism relation of noncompact surfaces with pants decompositions., Comment: 13 pages, 12 figures more...
DuBois, Natalie, Eufemia, Chris, Johannes, Jeff, and Zomback, Jenna
Subjects
Mathematics - Geometric Topology, 57M25, 57M27
Abstract
In links with two components there are three different types of crossings: self-crossings in the first component, self crossings in the second component, and crossings between components. In this paper we examine the minimum number of crossing changes needed to unlink without changing the crossings between components. We restrict our attention to unlinking two component links with linking number zero and both components unknotted. We provide data for links with no more than ten crossings and general results about asymmetry of unlinking between components., Comment: 10 pages, 12 figures more...