Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-27T10:19:40.559Z Has data issue: false hasContentIssue false
  • English
  • Français

The torsion of the group of homeomorphisms of powers of the long line

Part of: Topological manifolds Classical Topics in Algebraic Topology Set theory

Published online by Cambridge University Press:  09 April 2009

Satya Deo  and
David Gauld
Satya Deo
Affiliation:
Department of Mathematics R. D. UniversityJabalpur (M. P.) 482001India e-mail: sdt@rdunijb.ren.nic.in
David Gauld
Affiliation:
Department of Mathematics The University of AucklandPrivate Bag 92019 AucklandNew Zealand e-mail: gauld@math.auckland.ac.nz
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

By blending techniques from set theory and algebraic topology we investigate the order of any homeomorphism of the nth power of the long ray or long line L having finite order, finding all possible orders when n = 1, 2, 3 or 4 in the first case and when n = 1 or 2 in the second. We also show that all finite powers of L are acyclic with respect to Alexander-Spanier cohomology.

Keywords

long linelong rayAlexander-Spanier cohomologytorsion of homeomorphisms

MSC classification

Secondary: 55M35: Finite groups of transformations (including Smith theory) 57N65: Algebraic topology of manifolds 57N80: Stratifications 57S17: Finite transformation groups 03E75: Applications of set theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 70 , Issue 3 , June 2001 , pp. 311 - 322
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Borel, A., Seminar on transformation groups, Ann. of Math. Stud. 46 (Princeton University Press, Princeton, 1960).Google Scholar
[2]Bredon, G. E., Introduction to compact transformation groups (Academic Press, New York, 1972).Google Scholar
[3]Bredon, G. E., Sheaf theory, 2nd edition (Springer, New York, 1997).CrossRefGoogle Scholar
[4]Gauld, D., ‘Homeomorphisms of 1-manifolds and ω-bounded 2-manifolds’, in: Papers on general topology and applications (Ann. New York Acad. Sci., New York, 1993) pp. 142–149.Google Scholar
[5]Kunen, K., Set theory, an introduction to independence proofs (North Holland, Amsterdam, 1980).Google Scholar
[6]Spanier, E. H., Algebraic topology (McGraw Hill, New York, 1966).Google Scholar