Monotone, monotone open, and light open mappings on manifolds

<p>Let M^m and Nⁿ be compact connected p.1. (piecewise linear) manifolds with m ≥ 3. The first result is that a mapping f from M to N is homotopic to a monotone map of M onto N if and only if f_*:π1(M) -—> π1 (N) is a surjection (mapping = map = continuous function). There are two results of a technical nature which contain sufficient conditions for the existence of monotone open and light open maps between p.1. manifolds. These provide the following two results. If f is a monotone map of M^m onto Nⁿ and m ≥ 3, then f can be uniformly approximated by monotone open maps of M onto N. If f is an open map of M^m onto Nⁿ and n≥ m ≥ 3, then f can be uniformly approximated by light open maps of M onto N. An immediate corollary is that if n≥ m ≥ 3 and f is a map from M^m to Nⁿ with f*:π1(M) -—> π1 (N) a surjection, then f is homotopic to a light open map of M onto N.</p> <p>This work is motivated by the recent work of David C. Wilson where he constructs such mappings from manifolds onto cells; the methods of proof are similar.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematical Sciences

Year

1973

Author dc:creator

• Walsh, John J.

Contributors dc:contributor

• Louis F. McAuley
• Patricia McAuley
• Dick Wick Hall

• Topology Manifolds (Mathematics)
• Conformal mapping

Repository record dc:identifier

https://orb.binghamton.edu/dissertation_and_theses/214

OAI identifier oai:identifier

oai:orb.binghamton.edu:dissertation_and_theses-1220