Uniform and Lipschitz homotopy classes of maps

Author:
Sol Schwartzman

Journal:
Trans. Amer. Math. Soc. **354** (2002), 5039-5047

MSC (2000):
Primary 54E15, 55N10

DOI:
https://doi.org/10.1090/S0002-9947-02-03107-0

Published electronically:
August 1, 2002

MathSciNet review:
1926848

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Abstract | References | Similar Articles | Additional Information

Abstract: If is a compact connected polyhedron, we associate with each uniform homotopy class of uniformly continuous mappings from the real line into an element of where is the space of uniformly continuous functions from to and is the subspace of bounded uniformly continuous functions. This map from uniform homotopy classes of functions to is surjective. If is the -dimensional torus, it is bijective, while if is a compact orientable surface of genus , it is not injective.

In higher dimensions we have to consider smooth Lipschitz homotopy classes of smooth Lipschitz maps from suitable Riemannian manifolds to compact smooth manifolds With each such Lipschitz homotopy class we associate an element of where is the dimension of is the space of bounded continuous functions from the positive real axis to and is the set of all such that

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Additional Information

**Sol Schwartzman**

Affiliation:
Department of Mathematics, University of Rhode Island, Kingston, Rhode Island 02881

DOI:
https://doi.org/10.1090/S0002-9947-02-03107-0

Received by editor(s):
April 1, 2000

Received by editor(s) in revised form:
May 22, 2002

Published electronically:
August 1, 2002

Article copyright:
© Copyright 2002
American Mathematical Society