Geometry & Topology Volume 27, issue 5 (2023)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

A sharp lower bound on fixed points of surface symplectomorphisms in each mapping class

Andrew Cotton-Clay

Geometry & Topology 27 (2023) 1657–1690

DOI: 10.2140/gt.2023.27.1657

Bibliography

1	A Cotton-Clay, Symplectic Floer homology of area-preserving surface diffeomorphisms, Geom. Topol. 13 (2009) 2619 MR2529943
2	A W Cotton-Clay, Symplectic Floer homology of area-preserving surface diffeomorphisms and sharp fixed point bounds, PhD thesis, University of California, Berkeley (2009) MR2713919
3	S Dostoglou, D A Salamon, Self-dual instantons and holomorphic curves, Ann. of Math. 139 (1994) 581 MR1283871
4	A Fathi, F Laudenbach, V Poénaru, editors, Travaux de Thurston sur les surfaces, 66–67, Soc. Math. France (1979) 284 MR568308
5	A Floer, H Hofer, D Salamon, Transversality in elliptic Morse theory for the symplectic action, Duke Math. J. 80 (1995) 251 MR1360618
6	M Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307 MR809718
7	K Honda, W H Kazez, G Matić, Right-veering diffeomorphisms of compact surfaces with boundary, Invent. Math. 169 (2007) 427 MR2318562
8	M Hutchings, An index inequality for embedded pseudoholomorphic curves in symplectizations, J. Eur. Math. Soc. 4 (2002) 313 MR1941088
9	M Hutchings, M Sullivan, Rounding corners of polygons and the embedded contact homology of T³, Geom. Topol. 10 (2006) 169 MR2207793
10	B J Jiang, J H Guo, Fixed points of surface diffeomorphisms, Pacific J. Math. 160 (1993) 67 MR1227504
11	Y J Lee, Heegaard splittings and Seiberg–Witten monopoles, from: "Geometry and topology of manifolds", Fields Inst. Commun. 47, Amer. Math. Soc. (2005) 173 MR2189932
12	Y J Lee, Reidemeister torsion in Floer–Novikov theory and counting pseudo-holomorphic tori, I, J. Symplectic Geom. 3 (2005) 221 MR2199540
13	Y J Lee, Reidemeister torsion in Floer–Novikov theory and counting pseudo-holomorphic tori, II, J. Symplectic Geom. 3 (2005) 385 MR2198782
14	Y J Lee, C H Taubes, Periodic Floer homology and Seiberg–Witten–Floer cohomology, J. Symplectic Geom. 10 (2012) 81 MR2904033
15	T Perutz, Lagrangian matching invariants for fibred four-manifolds, II, Geom. Topol. 12 (2008) 1461 MR2421133
16	J Robbin, D Salamon, The spectral flow and the Maslov index, Bull. London Math. Soc. 27 (1995) 1 MR1331677
17	M Schwarz, A quantum cup-length estimate for symplectic fixed points, Invent. Math. 133 (1998) 353 MR1632778
18	P Seidel, Symplectic Floer homology and the mapping class group, Pacific J. Math. 206 (2002) 219 MR1924827
19	C H Taubes, The structure of pseudoholomorphic subvarieties for a degenerate almost complex structure and symplectic form on S¹ × B³, Geom. Topol. 2 (1998) 221 MR1658028
20	W P Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. 19 (1988) 417 MR956596
21	M Usher, Vortices and a TQFT for Lefschetz fibrations on 4–manifolds, Algebr. Geom. Topol. 6 (2006) 1677 MR2263047
22	L H Vân, K Ono, Symplectic fixed points, the Calabi invariant and Novikov homology, Topology 34 (1995) 155 MR1308493