The periodic Floer homology of a Dehn twist

Hutchings, Michael; Sullivan, Michael G

doi:10.2140/agt.2005.5.301

Hutchings, Michael ¹ ; Sullivan, Michael G ²

¹Department of Mathematics, University of California, Berkeley CA 94720-3840, USA
²Department of Mathematics and Statistics, University of Massachusetts, Amherst MA 01003-9305, USA

Algebraic and Geometric Topology, Tome 5 (2005) no. 1, pp. 301-354

Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

Résumé

The periodic Floer homology of a surface symplectomorphism, defined by the first author and M. Thaddeus, is the homology of a chain complex which is generated by certain unions of periodic orbits, and whose differential counts certain embedded pseudoholomorphic curves in ℝ cross the mapping torus. It is conjectured to recover the Seiberg-Witten Floer homology of the mapping torus for most spin-c structures, and is related to a variant of contact homology. In this paper we compute the periodic Floer homology of some Dehn twists.

DOI : 10.2140/agt.2005.5.301

Keywords: periodic Floer homology, Dehn twist, surface symplectomorphism

Affiliations des auteurs :

Hutchings, Michael ¹ ; Sullivan, Michael G ²

¹ Department of Mathematics, University of California, Berkeley CA 94720-3840, USA
² Department of Mathematics and Statistics, University of Massachusetts, Amherst MA 01003-9305, USA

@article{10_2140_agt_2005_5_301,
     author = {Hutchings, Michael and Sullivan, Michael G},
     title = {The periodic {Floer} homology of a {Dehn} twist},
     journal = {Algebraic and Geometric Topology},
     pages = {301--354},
     year = {2005},
     volume = {5},
     number = {1},
     doi = {10.2140/agt.2005.5.301},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2005.5.301/}
}

TY  - JOUR
AU  - Hutchings, Michael
AU  - Sullivan, Michael G
TI  - The periodic Floer homology of a Dehn twist
JO  - Algebraic and Geometric Topology
PY  - 2005
SP  - 301
EP  - 354
VL  - 5
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2005.5.301/
DO  - 10.2140/agt.2005.5.301
ID  - 10_2140_agt_2005_5_301
ER  -

%0 Journal Article
%A Hutchings, Michael
%A Sullivan, Michael G
%T The periodic Floer homology of a Dehn twist
%J Algebraic and Geometric Topology
%D 2005
%P 301-354
%V 5
%N 1
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2005.5.301/
%R 10.2140/agt.2005.5.301
%F 10_2140_agt_2005_5_301

Hutchings, Michael; Sullivan, Michael G. The periodic Floer homology of a Dehn twist. Algebraic and Geometric Topology, Tome 5 (2005) no. 1, pp. 301-354. doi: 10.2140/agt.2005.5.301

Bibliographie
Cité par

[1] F Bourgeois, A Morse–Bott approach to contact homology, from: "Symplectic and contact topology : interactions and perspectives (Toronto, ON/Montreal, QC, 2001)", Fields Inst. Commun. 35, Amer. Math. Soc. (2003) 55

[2] K Cieliebak, I Mundet I Riera, D A Salamon, Equivariant moduli problems, branched manifolds, and the Euler class, Topology 42 (2003) 641

[3] S K Donaldson, Floer homology and algebraic geometry, from: "Vector bundles in algebraic geometry (Durham, 1993)", London Math. Soc. Lecture Note Ser. 208, Cambridge Univ. Press (1995) 119

[4] E Eftekhary, Floer homology of certain pseudo–Anosov maps, J. Symplectic Geom. 2 (2004) 357

[5] Y Eliashberg, A Givental, H Hofer, Introduction to symplectic field theory, Geom. Funct. Anal. (2000) 560

[6] A Floer, Morse theory for Lagrangian intersections, J. Differential Geom. 28 (1988) 513

[7] K Fukaya, K Ono, Arnold conjecture and Gromov–Witten invariant, Topology 38 (1999) 933

[8] R Gautschi, Floer homology of algebraically finite mapping classes, J. Symplectic Geom. 1 (2003) 715

[9] M Hutchings, An index inequality for embedded pseudoholomorphic curves in symplectizations, J. Eur. Math. Soc. (JEMS) 4 (2002) 313

[10] M Hutchings, Y J Lee, Circle-valued Morse theory, Reidemeister torsion, and Seiberg–Witten invariants of 3–manifolds, Topology 38 (1999) 861

[11] M Hutchings, M Sullivan, Rounding corners of polygons and the embedded contact homology of T3, Geom. Topol. 10 (2006) 169

[12] M Hutchings, M Thaddeus, Periodic Floer homology, in preparation

[13] S Jabuka, T Mark, Heegaard Floer homology of certain mapping tori, Algebr. Geom. Topol. 4 (2004) 685

[14] Y J Lee, Reidemeister torsion in Floer–Novikov theory and counting pseudo-holomorphic tori I, J. Symplectic Geom. 3 (2005) 221

[15] D Mcduff, Singularities and positivity of intersections of J–holomorphic curves, from: "Holomorphic curves in symplectic geometry", Progr. Math. 117, Birkhäuser (1994) 191

[16] P Ozsváth, Z Szabó, Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. (2) 159 (2004) 1027

[17] P Ozsváth, Z Szabó, Holomorphic disks and three-manifold invariants: properties and applications, Ann. of Math. (2) 159 (2004) 1159

[18] P Ozsváth, Z Szabó, Holomorphic disks and knot invariants, Adv. Math. 186 (2004) 58

[19] D A Salamon, Seiberg–Witten invariants of mapping tori, symplectic fixed points, and Lefschetz numbers, from: "Proceedings of 6th Gökova Geometry–Topology Conference" (1999) 117

[20] M Schwarz, Cohomology operations from S1 cobordisms in Floer homology, thesis, ETH Zürich (1995)

[21] P Seidel, The symplectic Floer homology of a Dehn twist, Math. Res. Lett. 3 (1996) 829

[22] P Seidel, More about vanishing cycles and mutation, from: "Symplectic geometry and mirror symmetry (Seoul, 2000)", World Sci. Publ., River Edge, NJ (2001) 429

[23] M G Sullivan, K–theoretic invariants for Floer homology, Geom. Funct. Anal. 12 (2002) 810

[24] C H Taubes, The Seiberg–Witten and Gromov invariants, Math. Res. Lett. 2 (1995) 221

[25] C H Taubes, A compendium of pseudoholomorphic beasts in R × (S1 × S2), Geom. Topol. 6 (2002) 657

[26] C H Taubes, Pseudoholomorphic punctured spheres in R×(S1×S2) : properties and existence, Geom. Topol. 10 (2006) 785

Cité par Sources :

Parcourir par

Geodesic

Parcourir par