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

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

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
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Abstract

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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

Information

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

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