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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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R-torsion and zeta functions for analytic Anosov flows on 3-manifolds
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by Héctor Sánchez-Morgado PDF
Trans. Amer. Math. Soc. 348 (1996), 963-973 Request permission

Abstract:

We improve previous results relating R-torsion, for an acyclic representation of the fundamental group, with a special value of the torsion zeta function of an analytic Anosov flow on a 3-manifold. By using the new techniques of Rugh and Fried we get rid of the unpleasent assumptions about the regularity of the invariant foliations.
References
  • David Fried, Fuchsian groups and Reidemeister torsion, The Selberg trace formula and related topics (Brunswick, Maine, 1984) Contemp. Math., vol. 53, Amer. Math. Soc., Providence, RI, 1986, pp. 141–163. MR 853556, DOI 10.1090/conm/053/853556
  • David Fried, Lefschetz formulas for flows, The Lefschetz centennial conference, Part III (Mexico City, 1984) Contemp. Math., vol. 58, Amer. Math. Soc., Providence, RI, 1987, pp. 19–69. MR 893856
  • Fried, D. Meromorphic Zeta Functions for Analytic Flows. Preprint 1993.
  • Nicolai T. A. Haydn, Meromorphic extension of the zeta function for Axiom A flows, Ergodic Theory Dynam. Systems 10 (1990), no. 2, 347–360. MR 1062762, DOI 10.1017/S0143385700005587
  • Ratner, M. Markov decomposition for a Y-flow on a three-dimensional manifold. Math. Notes 6 (1968) 880-886.
  • David Ruelle, The thermodynamic formalism for expanding maps, Comm. Math. Phys. 125 (1989), no. 2, 239–262. MR 1016871, DOI 10.1007/BF01217908
  • Hans H. Rugh, The correlation spectrum for hyperbolic analytic maps, Nonlinearity 5 (1992), no. 6, 1237–1263. MR 1192517, DOI 10.1088/0951-7715/5/6/003
  • Rugh, H. Generalized Fredholm Determinants and Selberg Zeta Functions for Axiom A Dynamical Systems. To appear in Ergod. Th. and Dynam. Sys.
  • Sánchez-Morgado, H. Lefschetz formulae for Anosov flows on 3-manifolds. Ergod. Th. and Dynam. Sys. 13 (1993) 335-347.
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Additional Information
  • Héctor Sánchez-Morgado
  • Affiliation: Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria C. P. 04510, México D. F., México
  • MR Author ID: 340702
  • ORCID: 0000-0003-3981-408X
  • Email: hector@gauss.matem.unam.mx
  • Received by editor(s): November 18, 1994
  • Additional Notes: Partially supported by DGAPA-UNAM IN-103792
  • © Copyright 1996 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 348 (1996), 963-973
  • MSC (1991): Primary 58F15, 58F20, 58G10
  • DOI: https://doi.org/10.1090/S0002-9947-96-01611-X
  • MathSciNet review: 1348868