University of Birmingham > Talks@bham > Topology and Dynamics seminar > Locally finite trees and the topological minor relation

Locally finite trees and the topological minor relation

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact Tony Samuel.

Nash-Williams showed that the collection of locally finite trees under the topological minor relation results in a BQO (better-quasi-order). Naturally, two interesting questions arise:

1. What is the number \lambda of topological types of locally finite trees?

2. What are the possible sizes of an equivalence class of locally finite trees?

For (1), clearly, \omega_0 \leq \lambda \leq c and Matthiesen refined it to \omega_1 \leq \lambda \leq c. Thus, this question becomes non-trivial in the absence of the Continuum Hypothesis. In this talk we address both questions by showing – entirely within ZFC - that for a large collection of locally finite trees that includes those with countably many rays:

- \lambda = \omega_1, and

- the size of an equivalence class can only be either 1 or c.

This talk is part of the Topology and Dynamics seminar series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

Talks@bham, University of Birmingham. Contact Us | Help and Documentation | Privacy and Publicity.
talks@bham is based on talks.cam from the University of Cambridge.