Functorial properties of Putnam's homology theory for Smale spaces

Article, Preprint English OPEN
Deeley, Robin J. ; Killough, D. Brady ; Whittaker, Michael F. (2016)
  • Publisher: Cambridge University Press
  • Related identifiers: doi: 10.1017/etds.2014.134
  • Subject: QA | 37D20 (Primary), 37B10 (Secondary) | Mathematics - Dynamical Systems | Mathematics - K-Theory and Homology
    arxiv: Mathematics::Dynamical Systems | Mathematics::Algebraic Topology | Mathematics::Category Theory

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.
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    [6] S. Smale, Differentiable dynamical systems, Bull. A.M.S. 73 (1967), 747-817. Robin J. Deeley, Laboratorie de Mathematiques, Universite Blaise Pascal, Clermont-Ferrand II, France E-mail address: robin.deeley@gmail.com Brady Killough, Mathematics, Physics and Engineering, Mount Royal University, Calgary, Alberta, Canada T3E 6K6 E-mail address: bkillough@mtroyal.ca Michael F. Whittaker, School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia E-mail address: mfwhittaker@gmail.com

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