Sheaves that are locally constant with applications to homology manifolds

  • Jerzy Dydak
  • John Walsh
Conference paper

DOI: 10.1007/BFb0081420

Part of the Lecture Notes in Mathematics book series (LNM, volume 1283)
Cite this paper as:
Dydak J., Walsh J. (1987) Sheaves that are locally constant with applications to homology manifolds. In: Mardešić S., Segal J. (eds) Geometric Topology and Shape Theory. Lecture Notes in Mathematics, vol 1283. Springer, Berlin, Heidelberg

Abstract

Analyses are made that establish a connection between properties of presheaves and the constancy of the induced (or associated) sheaves. While the analyses applies regardiess of the source of the presheaves, the applications involve either the homology presheaf and sheaf of a space or the cohomology presheaf and sheaf of a continuous function. Amongst the applications is an elementary proof that homology manifolds are locally orientable; that is, the orientation sheaf is locally constant. Additional applications appearing elsewhere include determining the homological local connectivity of decomposition spaces and providing dimension estimates of the images of closed mappings.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Jerzy Dydak
    • 1
    • 2
  • John Walsh
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of TennesseeKnoxville
  2. 2.Department of MathematicsUniversity of CaliforniaRiverside

Personalised recommendations