A note on homology for Smale spaces
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Standard
A note on homology for Smale spaces. / Proietti, Valerio.
I: Groups, Geometry, and Dynamics, Bind 14, Nr. 3, 2020, s. 813-836.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
TY - JOUR
T1 - A note on homology for Smale spaces
AU - Proietti, Valerio
PY - 2020
Y1 - 2020
N2 - We collect three observations on the homology for Smale spaces defined by Putnam. The definition of such homology groups involves four complexes. It is shown here that a simple convergence theorem for spectral sequences can be used to prove that all complexes yield the same homology. Furthermore, we introduce a simplicial framework by which the various complexes can be understood as suitable "symmetric" Moore complexes associated to the simplicial structure. The last section discusses projective resolutions in the context of dynamical systems. It is shown that the projective cover of a Smale space is realized by the system of shift spaces and factor maps onto it.
AB - We collect three observations on the homology for Smale spaces defined by Putnam. The definition of such homology groups involves four complexes. It is shown here that a simple convergence theorem for spectral sequences can be used to prove that all complexes yield the same homology. Furthermore, we introduce a simplicial framework by which the various complexes can be understood as suitable "symmetric" Moore complexes associated to the simplicial structure. The last section discusses projective resolutions in the context of dynamical systems. It is shown that the projective cover of a Smale space is realized by the system of shift spaces and factor maps onto it.
U2 - 10.4171/GGD/564
DO - 10.4171/GGD/564
M3 - Journal article
VL - 14
SP - 813
EP - 836
JO - Groups, Geometry, and Dynamics
JF - Groups, Geometry, and Dynamics
SN - 1661-7207
IS - 3
ER -
ID: 257658961