Reidemeister torsion of a symplectic complex
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Reidemeister torsion of a symplectic complex

Yaşar Sözen

Source: Osaka J. Math. Volume 45, Number 1 (2008), 1-39.

Abstract

We consider a claim mentioned in [33] p.187 about the relation between a symplectic chain complex with $\omega$-compatible bases and Reidemeister Torsion of it. This is an explanation of it.

Primary Subjects: 32G15, 57R30

Full-text: Access granted (open access)

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.ojm/1205503554

References

L.V. Ahlfors: Some remarks on Teichmüller's space of Riemann surfaces, Ann. of Math. (2) 74 (1961), 171--191.
Mathematical Reviews (MathSciNet): MR204641
Digital Object Identifier: doi:10.2307/1970309
JSTOR: links.jstor.org
F. Bonahon: Closed Curves on Surfaces, monograph in preparation.
F. Bonahon: Shearing hyperbolic surfaces, bending pleated surfaces and Thurston's symplectic form, Ann. Fac. Sci. Toulouse Math. (6) 5 (1996), 233--297.
Mathematical Reviews (MathSciNet): MR1413855
F. Bonahon: Geodesic laminations with transverse Hölder distributions, Ann. Sci. École Norm. Sup. (4) 30 (1997), 205--240.
Mathematical Reviews (MathSciNet): MR1432054
Digital Object Identifier: doi:10.1016/S0012-9593(97)89919-3
F. Bonahon: Transverse Hölder distributions for geodesic laminations, Topology 36 (1997), 103--122.
Mathematical Reviews (MathSciNet): MR1410466
Digital Object Identifier: doi:10.1016/0040-9383(96)00001-8
R.D. Canary, D.B.A. Epstein and P. Green: Notes on notes of Thurston; in Analytical and Geometric Aspects of Hyperbolic Space (Coventry/Durham, 1984), London Math. Soc. Lecture Note Ser. 111, Cambridge Univ. Press, Cambridge, 1987, 3--92.
Mathematical Reviews (MathSciNet): MR903850
Zentralblatt MATH: 0612.57009
T.A. Chapman: Compact Hilbert cube manifolds and the invariance of Whitehead torsion, Bull. Amer. Math. Soc. 79 (1973), 52--56.
Mathematical Reviews (MathSciNet): MR346794
Digital Object Identifier: doi:10.1090/S0002-9904-1973-13087-3
T.A. Chapman: Topological invariance of Whitehead torsion, Amer. J. Math. 96 (1974), 488--497.
Mathematical Reviews (MathSciNet): MR391109
Digital Object Identifier: doi:10.2307/2373556
JSTOR: links.jstor.org
G. de Rham: Reidemeister's torsion invariant and rotations of $S^n$; in Differential Analysis, Bombay Colloq., Oxford Univ. Press, London, 1964, 27--36.
Mathematical Reviews (MathSciNet): MR190945
Zentralblatt MATH: 0145.44004
A. Fel'shtyn: Dynamical Zeta Functions, Nielsen Theory and Reidemeister Torsion, Mem. Amer. Math. Soc. 147, 2000.
Mathematical Reviews (MathSciNet): MR1697460
W. Franz: Über die Torsion einer Überdeckung, J. Reine Angew. Math. 173 (1935), 245--254.
D. Fried: Homological identities for closed orbits, Invent. Math. 71 (1983), 419--442.
Mathematical Reviews (MathSciNet): MR689651
Digital Object Identifier: doi:10.1007/BF01389105
F.P. Gardiner and N. Lakic: Quasiconformal Teichmüller Theory, Mathematical Surveys and Monographs 76, Amer. Math. Soc., Providence, RI, 2000.
Mathematical Reviews (MathSciNet): MR1730906
W.M. Goldman: The symplectic nature of fundamental groups of surfaces, Adv. in Math. 54 (1984), 200--225.
Mathematical Reviews (MathSciNet): MR762512
Digital Object Identifier: doi:10.1016/0001-8708(84)90040-9
Y. Imayoshi and M. Taniguchi: An Introduction to Teichmüller Spaces, Springer-Verlag, Tokyo, 1992.
Mathematical Reviews (MathSciNet): MR1215481
M. Kapovich: Hyperbolic Manifolds and Discrete Groups, Progr. Math., 183, Birkhäuser Boston Inc., Boston, MA, 2001.
Mathematical Reviews (MathSciNet): MR1792613
Zentralblatt MATH: 0958.57001
R.C. Kirby and L.C. Siebenmann: On the triangulation of manifolds and the Hauptvermutung, Bull. Amer. Math. Soc. 75 (1969), 742--749.
Mathematical Reviews (MathSciNet): MR242166
Digital Object Identifier: doi:10.1090/S0002-9904-1969-12271-8
J. Milnor: A duality theorem for Reidemeister torsion, Ann. of Math. (2) 76 (1962), 137--147.
Mathematical Reviews (MathSciNet): MR141115
Digital Object Identifier: doi:10.2307/1970268
JSTOR: links.jstor.org
J. Milnor: Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966), 358--426.
Mathematical Reviews (MathSciNet): MR196736
Digital Object Identifier: doi:10.1090/S0002-9904-1966-11484-2
J. Milnor: Infinite cyclic coverings; in Conference on the Topology of Manifolds (Michigan State Univ., E. Lansing, Mich., 1967), Prindle, Weber & Schmidt, Boston, Mass., 1968, 115\nobreakdash--133.
Mathematical Reviews (MathSciNet): MR242163
Zentralblatt MATH: 0179.52302
R.C. Penner and J.L. Harer: Combinatorics of Train Tracks, Ann. of Math. Stud. 125, Princeton Univ. Press, Princeton, NJ, 1992.
Mathematical Reviews (MathSciNet): MR1144770
Zentralblatt MATH: 0765.57001
J. Porti: Torsion de Reidemeister pour les Variétés Hyperboliques, Mem. Amer. Math. Soc. 128, 1997.
Mathematical Reviews (MathSciNet): MR1396960
M.S. Raghunathan: Discrete Subgroups of Lie Groups, Springer-Verlag, New York, 1972.
Mathematical Reviews (MathSciNet): MR507234
Zentralblatt MATH: 0254.22005
K. Reidemeister: Homotopieringe und Linsenräume, Hamburger Abhandl 11 (1935), 102--109.
A.S. Schwarz: The partition function of degenerate quadratic functional and Ray-Singer invariants, Lett. Math. Phys. 2 (1977/78), 247--252.
Mathematical Reviews (MathSciNet): MR676337
Digital Object Identifier: doi:10.1007/BF00406412
Y. Sözen: Reidemeister torsion and Pfaffian of Thurston's symplectic form, submitted.
Y. Sözen and F. Bonahon: The Weil-Petersson and Thurston symplectic forms, Duke Math. J. 108 (2001), 581--597.
Mathematical Reviews (MathSciNet): MR1838662
Digital Object Identifier: doi:10.1215/S0012-7094-01-10836-3
Project Euclid: euclid.dmj/1091737184
\advance\xspaceskip-1pt W.P. Thurston: Minimal stretch maps between hyperbolic surfaces, preprint, math.GT/9801039.
A. Weil: On the moduli of Riemann surfaces, 1958 (to Emil Atrin), unpublished, Collected papers/André Weil, New York, Sipringer-Verlag, 1979, 381--389.
A. Weil: On discrete subgroups of Lie groups, Ann. of Math. (2) 72 (1960), 369--384.
Mathematical Reviews (MathSciNet): MR137792
Digital Object Identifier: doi:10.2307/1970140
JSTOR: links.jstor.org
A. Weil: Remarks on the cohomology of groups, Ann. of Math. (2) 80 (1964), 149--157.
Mathematical Reviews (MathSciNet): MR169956
Digital Object Identifier: doi:10.2307/1970495
JSTOR: links.jstor.org
E. Witten: Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989), 351--399.
Mathematical Reviews (MathSciNet): MR990772
Digital Object Identifier: doi:10.1007/BF01217730
Project Euclid: euclid.cmp/1104178138
E. Witten: On quantum gauge theories in two dimensions, Comm. Math. Phys. 141 (1991), 153--209.
Mathematical Reviews (MathSciNet): MR1133264
Digital Object Identifier: doi:10.1007/BF02100009
Project Euclid: euclid.cmp/1104248198
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