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Functorial properties of Putnam’s homology theory for Smale spaces

Published online by Cambridge University Press:  19 March 2015

ROBIN J. DEELEY ,
D. BRADY KILLOUGH  and
MICHAEL F. WHITTAKER
ROBIN J. DEELEY
Affiliation:
Laboratoire de Mathématiques, Université Blaise Pascal, Clermont-Ferrand II, France email robin.deeley@gmail.com
D. BRADY KILLOUGH
Affiliation:
Mathematics, Physics and Engineering, Mount Royal University, Calgary, Alberta, Canada T3E 6K6 email bkillough@mtroyal.ca
MICHAEL F. WHITTAKER
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia email mfwhittaker@gmail.com
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Abstract

We investigate functorial properties of Putnam’s homology theory for Smale spaces. Our analysis shows that the addition of a conjugacy condition is necessary to ensure functoriality. Several examples are discussed that elucidate the need for our additional hypotheses. Our second main result is a natural generalization of Putnam’s Pullback Lemma from shifts of finite type to non-wandering Smale spaces.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 5 , August 2016 , pp. 1411 - 1440
Copyright
© Cambridge University Press, 2015 

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