Algebraic & Geometric Topology Volume 25, issue 7 (2025)

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ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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Product and coproduct on fixed point Floer homology of positive Dehn twists

Yuan Yao and Ziwen Zhao

Algebraic & Geometric Topology 25 (2025) 3875–3919

DOI: 10.2140/agt.2025.25.3875

Bibliography

1	A Abbondandolo, M Schwarz, Floer homology of cotangent bundles and the loop product, Geom. Topol. 14 (2010) 1569 MR2679580
2	F Bourgeois, Y Eliashberg, H Hofer, K Wysocki, E Zehnder, Compactness results in symplectic field theory, Geom. Topol. 7 (2003) 799 MR2026549
3	G Chen, On cobordism maps on periodic Floer homology, Algebr. Geom. Topol. 21 (2021) 1 MR4224736
4	K Cieliebak, J Latschev, The role of string topology in symplectic field theory, from: "New perspectives and challenges in symplectic field theory" (editors M Abreu, F Lalonde, L Polterovich), CRM Proc. Lecture Notes 49, Amer. Math. Soc. (2009) 113 MR2555935
5	V Colin, P Ghiggini, K Honda, Y Yao, Morse–Bott gluing, MR4974986
6	A Cotton-Clay, Symplectic Floer homology of area-preserving surface diffeomorphisms, Geom. Topol. 13 (2009) 2619 MR2529943
7	S Dostoglou, D A Salamon, Self-dual instantons and holomorphic curves, Ann. of Math. (2) 139 (1994) 581 MR1283871
8	E Eftekhary, Floer homology of certain pseudo-Anosov maps, J. Symplectic Geom. 2 (2004) 357 MR2131640
9	U Frauenfelder, F Schlenk, Hamiltonian dynamics on convex symplectic manifolds, Israel J. Math. 159 (2007) 1 MR2342472
10	R Gautschi, Floer homology of algebraically finite mapping classes, J. Symplectic Geom. 1 (2003) 715 MR2039162
11	H Hofer, Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three, Invent. Math. 114 (1993) 515 MR1244912
12	M Hutchings, M Sullivan, The periodic Floer homology of a Dehn twist, Algebr. Geom. Topol. 5 (2005) 301 MR2135555
13	M Hutchings, M Sullivan, Rounding corners of polygons and the embedded contact homology of T³, Geom. Topol. 10 (2006) 169 MR2207793
14	S Lanzat, Hamiltonian Floer homology for compact convex symplectic manifolds, Beitr. Algebra Geom. 57 (2016) 361 MR3493995
15	D McDuff, D Salamon, J-holomorphic curves and symplectic topology, 52, Amer. Math. Soc. (2012) MR2954391
16	R Pedrotti, Fixed point Floer cohomology of disjoint Dehn twists on a w⁺-monotone manifold with rational symplectic form, J. Symplectic Geom. 22 (2024) 549 MR4819507
17	S Piunikhin, D Salamon, M Schwarz, Symplectic Floer–Donaldson theory and quantum cohomology, from: "Contact and symplectic geometry" (editor C B Thomas), Publ. Newton Inst. 8, Cambridge Univ. Press (1996) 171 MR1432464
18	M Poźniak, Floer homology, Novikov rings and clean intersections, PhD thesis, University of Warwick (1994)
19	J H Rooney, On cobordism maps in embedded contact homology, PhD thesis, University of California, Los Angeles (2018) MR3828585
20	M Schwarz, Cohomology operations from S¹-cobordisms in Floer homology, PhD thesis, ETH Zürich (1995)
21	P Seidel, The symplectic Floer homology of a Dehn twist, Math. Res. Lett. 3 (1996) 829 MR1426539
22	P Seidel, Floer homology and the symplectic isotopy problem, PhD thesis, Oxford University (1997)
23	P Seidel, Symplectic Floer homology and the mapping class group, Pacific J. Math. 206 (2002) 219 MR1924827
24	C Wendl, Automatic transversality and orbifolds of punctured holomorphic curves in dimension four, Comment. Math. Helv. 85 (2010) 347 MR2595183
25	C Wendl, Lectures on symplectic field theory, preprint (2016)
26	Y Yao, From cascades to J-holomorphic curves and back, (2022) arXiv:2206.04334