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ISSN 1088-6826(e) ISSN 0002-9939(p)

Reidemeister torsion of $T^{2}$ -bundles over $S^{1}$ for $SL(2;\mathbf{C})$ -representations

Author(s): Teruaki Kitano
Journal: Proc. Amer. Math. Soc. 128 (2000), 3075-3079.
MSC (1991): Primary 57M05, 57M50, 57Q10
Posted: March 3, 2000
MathSciNet review: 1664382
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Abstract: We compute the $SL(2,\mathbf{C})$ -Reidemeister torsion of torus bundles over $S^{1}$ which monodromies are hyperbolic elements in $SL(2,\mathbf{Z})$ .

References:

1.: D. Johnson, A geometric form of Casson invariant and its connection to Reidemeister torsion, unpublished lecture notes.
2.: T. Kitano, Reidemeister torsion of Seifert fibered spaces for SL(2;C) representations, Tokyo J. of Math. 17 (1994), 59-74. MR 95c:57040
3.: -, Reidemeister torsion of the figure-eight knot exterior for $SL(2;\text{\bf C})$ -representations, Osaka J. of Math. 31 (1994), 523-532. MR 95i:57011
4.: -, On the Reidemeister torsion of Seifert fibered spaces for $SL(n;\text{\bf C})$ -representations, Kobe J. Math. 13 (1996), 133-144. MR 98b:57036
5.: J. Milnor, Two complexes which are homeomorphic but combinatorially distinct, Ann. of Math. 74 (1961), 575-590. MR 24:A2961
6.: -, A duality theorem for Reidemeister torsion, Ann. of Math. 76 (1962), 137-147. MR 25:4526
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Additional Information:

Teruaki Kitano
Affiliation: Ecole Normale Superieure de Lyon UMPA, 46 Allee d'Italie 69364 Lyon, France
Address at time of publication: Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo, Japan
Email: tkitano@umpa.ens-lyon.fr, kitano@math.titech.ac.jp

DOI: 10.1090/S0002-9939-00-05349-1
PII: S 0002-9939(00)05349-1
Keywords: Reidemeister torsion, torus bundle, $SL(2;\mathbf{C})$-representation.
Received by editor(s): April 27, 1998
Received by editor(s) in revised form: November 3, 1998
Posted: March 3, 2000
Additional Notes: The author was supported in part by JSPS research fellowships and the Fuujukai Foundation
Communicated by: Ronald A. Fintushel
Copyright of article: Copyright 2000, American Mathematical Society

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