Homeomorphisms and Dynamics on Non-metrisable Manifolds

David Gauld ()
Additional contact information
David Gauld: University of Auckland, Department of Mathematics

Chapter Chapter 5 in Non-metrisable Manifolds, 2014, pp 63-86 from Springer

Abstract: Abstract Our main goal in this chapter is the study of discrete dynamics on a manifold, i.e., homeomorphisms of the manifold. However in the first section we will look at some examples of continuous flows. We display a fixed-point free continuous flow on a version of the Prüfer manifold but at the same time show that any flow on the open long ray must have uncountably many fixed points. Our study of homeomorphisms of a non-metrisable manifold relates mainly to powers of the long line where we find the situation to be significantly different from the situation for powers of the real line: points where at least two coordinates agree combine to form barriers to the behaviour of homeomorphisms. We also display a surface whose group of homeomorphisms modulo isotopy is isomorphic to $${\mathbb Z}^{\mathbb Z}$$ Z Z .

Keywords: Homeomorphism; Form Barriers; Mapping Class Group; Open Line Segment; Direct Matrix (search for similar items in EconPapers)
Date: 2014
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-287-257-9_5

Ordering information: This item can be ordered from
http://www.springer.com/9789812872579

DOI: 10.1007/978-981-287-257-9_5

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().