Geometric Topology and Shape Theory
Volume 1283 of the series Lecture Notes in Mathematics pp 6587
Sheaves that are locally constant with applications to homology manifolds
 Jerzy DydakAffiliated withDepartment of Mathematics, University of TennesseeDepartment of Mathematics, University of California
 , John WalshAffiliated withDepartment of Mathematics, University of TennesseeDepartment of Mathematics, University of California
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.
 Title
 Sheaves that are locally constant with applications to homology manifolds
 Book Title
 Geometric Topology and Shape Theory
 Book Subtitle
 Proceedings of a Conference held in Dubrovnik, Yugoslavia, Sept. 29 – Oct. 10, 1986
 Pages
 pp 6587
 Copyright
 1987
 DOI
 10.1007/BFb0081420
 Print ISBN
 9783540184430
 Online ISBN
 9783540479758
 Series Title
 Lecture Notes in Mathematics
 Series Volume
 1283
 Series ISSN
 00758434
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
 Additional Links
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 Industry Sectors
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 Editors
 Authors

 Jerzy Dydak ^{(1)} ^{(2)}
 John Walsh ^{(1)} ^{(2)}
 Author Affiliations

 1. Department of Mathematics, University of Tennessee, 37996, Knoxville, TN
 2. Department of Mathematics, University of California, 92521, Riverside, CA
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