Additivity for parametrized topological Euler characteristic and Reidemeister torsion

Preprint English OPEN
Badzioch, Bernard ; Dorabiala, Wojciech (2005)
  • Subject: Mathematics - Algebraic Topology | 19D10, 55R70 | Mathematics - K-Theory and Homology
    arxiv: Mathematics::Geometric Topology | Mathematics::Algebraic Topology

Dwyer, Weiss, and Williams have recently defined the notions of parametrized topological Euler characteristic and parametrized topological Reidemeister torsion which are invariants of bundles of compact topological manifolds. We show that these invariants satisfy additivity formulas paralleling the additive properties of the classical Euler characteristic and Reidemeister torsion of finite CW-complexes.
  • References (24)
    24 references, page 1 of 3

    [1] J. M. Bismut and J. Lott. Flat vector bundles, direct images and higher real analytic torsion. J. Amer. Math. Soc., 8(2):291{363, 1995.

    [2] W. Dorabiala. The double coset theorem formula for algebraic K-theory of spaces. K-Theory, 25(3):251{276, 2002.

    [3] W. G. Dwyer. The centralizer decomposition of BG. In Algebraic topology: new trends in localization and periodicity (Sant Feliu de Gu xols, 1994), volume 136 of Progr. Math., pages 167{184. Birkhauser, Basel, 1996.

    [4] W. G. Dwyer and H. W. Henn. Homotopy theoretic methods in group cohomology. Advanced Courses in Mathematics. CRM Barcelona. Birkhauser Verlag, Basel, 2001.

    [5] W. G. Dwyer, M. Weiss, and B. Williams. A parametrized index theorem for the algebraic K-theory Euler class. Acta Math., 190(1):1{104, 2003.

    [6] R. D. Edwards and R. C. Kirby. Deformations of spaces of imbeddings. Ann. Math. (2), 93:63{88, 1971.

    [7] E. Dror Farjoun. Cellular spaces, null spaces and homotopy localization, volume 1622 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 1996.

    [8] S. Goette. Morse theory and higher torsion invariants I. preprint, 2003, available on Math arXiv math.DG/0111222.

    [9] S. Goette. Morse theory and higher torsion invariants II. preprint, 2003, available on Math arXiv math.DG/0305287.

    [10] K. Igusa. Axioms for higher torsion. preprint, 2005, available on Math arXiv math.KT/050250.

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