A note on homology for Smale spaces

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A note on homology for Smale spaces. / Proietti, Valerio.

In: Groups, Geometry, and Dynamics, Vol. 14, No. 3, 2020, p. 813-836.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Proietti, V 2020, 'A note on homology for Smale spaces', Groups, Geometry, and Dynamics, vol. 14, no. 3, pp. 813-836. https://doi.org/10.4171/GGD/564

APA

Proietti, V. (2020). A note on homology for Smale spaces. Groups, Geometry, and Dynamics, 14(3), 813-836. https://doi.org/10.4171/GGD/564

Vancouver

Proietti V. A note on homology for Smale spaces. Groups, Geometry, and Dynamics. 2020;14(3):813-836. https://doi.org/10.4171/GGD/564

Author

Proietti, Valerio. / A note on homology for Smale spaces. In: Groups, Geometry, and Dynamics. 2020 ; Vol. 14, No. 3. pp. 813-836.

Bibtex

@article{dd783f29771f4ba4b3b2966ce4bbd95e,
title = "A note on homology for Smale spaces",
abstract = "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.",
author = "Valerio Proietti",
year = "2020",
doi = "10.4171/GGD/564",
language = "English",
volume = "14",
pages = "813--836",
journal = "Groups, Geometry, and Dynamics",
issn = "1661-7207",
publisher = "European Mathematical Society Publishing House",
number = "3",

}

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