Hostname: page-component-848d4c4894-tn8tq Total loading time: 0 Render date: 2024-06-27T23:58:11.842Z Has data issue: false hasContentIssue false
  • English
  • Français

Controlled Homeomorphisms Over Nonpositively Curved Manifolds

Published online by Cambridge University Press:  20 November 2018

Bruce Hughes ,
Larry Taylor  and
Bruce Williams
Bruce Hughes
Affiliation:
Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240, USA, email: hughes@math.vanderbilt.edu
Larry Taylor
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, USA, email: taylor.2@nd.edu
Bruce Williams
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, USA, email: williams.4@nd.edu
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.

We obtain a homotopy splitting of the forget control map for controlled homeomorphisms over closed manifolds of nonpositive curvature.

Keywords

57N1553C2055R6557N37controlled topologycontrolled homeomorphismnonpositive curvatureNovikov conjectures
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 43 , Issue 3 , 01 September 2000 , pp. 343 - 354
Copyright
Copyright © Canadian Mathematical Society 2000

References

[1] Burghelea, D. and Lashof, R., Geometric transfer and the homotopy type of the automorphism groups of a manifold. Trans. Amer.Math. Soc. 269 (1982), 1–38.Google Scholar
[2] Farrell, F. T. and Jones, L. E., Topological rigidity of compact nonpositively curved manifolds. In: Differential Geometry: Riemannian Geometry (eds. R. Greene and S. T. Yau), Proc. Sympos. PureMath. 54(1993), Part III, 229–274.Google Scholar
[3] Hatcher, A. E., Concordance spaces, higher simple-homotopy theory, and applications. In: Algebraic and Geometric Topology (ed. R. J. Milgram), Proc. Sympos. Pure Math. 32(1978), Part I, 3–21.Google Scholar
[4] Hughes, B., Approximate fibrations on topological manifolds. MichiganMath. J. 26 (1985), 167–183.Google Scholar
[5] Hughes, B., Taylor, L. and Williams, B., Bundle theories for topological manifolds. Trans. Amer. Math. Soc. 319 (1990), 1–65.Google Scholar
[6] Hughes, B., Taylor, L. and Williams, B., Bounded homeomorphisms over Hadamard manifolds. Math. Scand. 73 (1993), 161–176.Google Scholar
[7] Hughes, B., Taylor, L. and Williams, B., Rigidity of fibrations over nonpositively curved manifolds. Topology 34 (1995), 565–574 Google Scholar
[8] Hughes, B., Taylor, L. and Williams, B., Splitting forget control maps. In preparation.Google Scholar
[9] Hughes, B., Taylor, L. and Williams, B., Controlled surgery theory over manifolds. In preparation.Google Scholar
[10] Rushing, T. B., Topological embeddings. Pure and Appl. Math. Series 52, Academic Press, New York, 1973.Google Scholar
[11] Weinberger, S. The topological classification of stratified spaces. Chicago Lectures inMathematics Series, Univ. of Chicago Press, Chicago, 1994.Google Scholar