Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Homological embedding properties of the fibers of a map and the dimension of its image


Author: John J. Walsh
Journal: Proc. Amer. Math. Soc. 85 (1982), 135-138
MSC: Primary 54F45; Secondary 55M10, 58B05
MathSciNet review: 647912
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A relationship is established between the homological codimension of the point inverses of a map and the dimension of its image. An infinite-dimensional version leads to the conclusion that the image of a proper map defined on Hilbert space cannot be countable dimensional. A finite-dimensional version yields: if $ g:{M^n} \to Y$ is a proper map, $ {M^n}$ is a $ G$-orientable $ n$-manifold without boundary, and $ \dim Y \leqslant k$, then there is a point $ y \in Y$ and an integer $ i \geqslant n - k$ such that $ {\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{H} ^i}({g^{ - 1}}(y);G) \ne 0$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54F45, 55M10, 58B05

Retrieve articles in all journals with MSC: 54F45, 55M10, 58B05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0647912-0
PII: S 0002-9939(1982)0647912-0
Keywords: $ Z$-set, infinite codimension, countable dimensional, homological embedding properties, dimension, Hilbert space, Hilbert cube
Article copyright: © Copyright 1982 American Mathematical Society