Geodesic
Floer Homology, Nielsen Theory, and Symplectic Zeta Functions
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic geometry: Methods, relations, and applications, Tome 246 (2004), pp. 283-296.

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A connection between symplectic Floer homology for surfaces and the Nielsen fixed point theory is described. New zeta functions and an asymptotic invariant of symplectic origin are defined. It is shown that special values of symplectic zeta functions are Reidemeister torsions. 
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A. L. Fel'shtyn. Floer Homology, Nielsen Theory, and Symplectic Zeta Functions. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic geometry: Methods, relations, and applications, Tome 246 (2004), pp. 283-296. http://geodesic.mathdoc.fr/item/TM_2004_246_a19/

[1] Brooks R., Brown R. F., Pak J., Taylor D. H., “Nielsen numbers of maps of tori”, Proc. Amer. Math. Soc., 52 (1975), 398–400 | DOI | MR | Zbl

[2] Dostoglou S., Salamon D. A., “Self-dual instantons and holomorphic curves”, Ann. Math., 139 (1994), 581–640 | DOI | MR | Zbl

[3] Earle C. J., Eells J., “The diffeomorphism group of a compact Riemann surface”, Bull. Amer. Math. Soc., 73 (1967), 557–559 | DOI | MR

[4] Fathi A., Laudenbach F., Poénaru V., Travaux de Thurston sur les surfaces, Astérisque, 66–67, Soc. Math. France, Paris, 1979 | MR

[5] Fel'shtyn A. L., Dynamical zeta functions, Nielsen theory and Reidemeister torsion, Mem. AMS, 147, no. 699, Amer. Math. Soc., Providence, RI, 2000, 146 pp. | MR

[6] Fel'shtyn A. L., “Dynamical zeta functions and asymptotic expansions in Nielsen theory”, Dynamical, spectral, and arithmetic zeta functions, Contemp. Math., 290, Amer. Math. Soc., Providence, RI, 2002, 67–79 | MR

[7] Floer A., “Morse theory for Lagrangian intersections”, J. Diff. Geom., 28 (1988), 513–547 | MR | Zbl

[8] Floer A., “Symplectic fixed points and holomorphic spheres”, Commun. Math. Phys., 120:2 (1989), 575–611 | DOI | MR | Zbl

[9] Fried D., “Lefschetz formulas for flows”, The Lefschetz centennial conference, Contemp. Math., 58, Amer. Math. Soc., Providence, RI, 1987, 19–69 | MR

[10] Gautschi R., Floer homology of algebraically finite mapping classes, , 2002 arXiv: /math.SG/0204032 | MR

[11] Gerber M., Katok A., “Smooth models of Thurston's pseudo-Anosov maps”, Ann. Sci. École Norm. Supér, 15 (1982), 173–204 | MR | Zbl

[12] Gromov M., “Pseudoholomorphic curves in symplectic manifolds”, Invent. Math., 82 (1985), 307–347 | DOI | MR | Zbl

[13] Jiang B., “Fixed point classes from a differentiable viewpoint”, Fixed point theory, Lect. Notes Math., 886, Springer, Berlin, 1981, 163–170 | MR

[14] Jiang B., “Estimation of the number of periodic orbits”, Pacif. J. Math., 172 (1996), 151–185 | MR | Zbl

[15] Jiang B., Guo J., “Fixed points of surface diffeomorphisms”, Pacif. J. Math., 160 (1993), 67–89 | MR | Zbl

[16] Ivanov N. V., “Chisla Nilsena otobrazhenii poverkhnosti”, Zap. nauch. sem. LOMI, 122, 1982, 56–65 | MR | Zbl

[17] Ivanov N. V., “Entropiya i chisla Nilsena”, DAN SSSR, 265:2 (1982), 284–287 | MR | Zbl

[18] Manning A., “Axiom $\mathrm{A}$ diffeomorphisms have rational zeta function”, Bull. London Math. Soc., 3 (1971), 215–220 | DOI | MR | Zbl

[19] McDuff D., Salamon D. A., Introduction to symplectic topology, Oxford Math. Monogr., Clarendon Press, Oxford, 1998 | MR

[20] Moser J., “On the volume elements on a manifold”, Trans. Amer. Math. Soc., 120 (1965), 286–294 | DOI | MR | Zbl

[21] Poźniak M., “Floer homology, Novikov rings and clean intersections”, Northern California symplectic geometry seminar, AMS Transl. Ser. 2, 196, Amer. Math. Soc., Providence, RI, 1999, 119–181 | MR | Zbl

[22] Seidel P., Symplectic Floer homology and the mapping class group, , 2001 arXiv: /math.SG/0010301 | MR

[23] Seidel P., Braids and symplectic four-manifolds with abelian fundamental group, , 2002 arXiv: /math.SG/0202135 | MR

[24] Thurston W. P., “On the geometry and dynamics of diffeomorphisms of surfaces”, Bull. Amer. Math. Soc., 19:2 (1988), 417–431 | DOI | MR | Zbl