Algebraic & Geometric Topology Volume 22, issue 3 (2022)

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ISSN (electronic): 1472-2739

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On the rank of $\pi_1(\mathrm{Ham})$

Andrés Pedroza

Algebraic & Geometric Topology 22 (2022) 1325–1336

DOI: 10.2140/agt.2022.22.1325

Bibliography

1	M Abreu, D McDuff, Topology of symplectomorphism groups of rational ruled surfaces, J. Amer. Math. Soc. 13 (2000) 971 MR1775741
2	S Anjos, S Eden, The homotopy Lie algebra of symplectomorphism groups of 3–fold blowups of (S² × S²,σ_std ⊕ σ_std), Michigan Math. J. 68 (2019) 71 MR3934605
3	S Anjos, M Pinsonnault, The homotopy Lie algebra of symplectomorphism groups of 3–fold blow-ups of the projective plane, Math. Z. 275 (2013) 245 MR3101807
4	D Auroux, I Smith, Fukaya categories of surfaces, spherical objects and mapping class groups, Forum Math. Sigma 9 (2021) MR4235165
5	J D Evans, Symplectic mapping class groups of some Stein and rational surfaces, J. Symplectic Geom. 9 (2011) 45 MR2787361
6	M Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307 MR809718
7	A Kislev, Compactly supported Hamiltonian loops with a non-zero Calabi invariant, Electron. Res. Announc. Math. Sci. 21 (2014) 80 MR3260131
8	F Lalonde, M Pinsonnault, The topology of the space of symplectic balls in rational 4–manifolds, Duke Math. J. 122 (2004) 347 MR2053755
9	J Li, T J Li, Symplectic (−2)–spheres and the symplectomorphism group of small rational 4–manifolds, Pacific J. Math. 304 (2020) 561 MR4062781
10	J Li, T J Li, W Wu, Symplectic (−2)–spheres and the symplectomorphism group of small rational 4–manifolds, II, preprint (2019) arXiv:1911.11073
11	D McDuff, The symplectomorphism group of a blow up, Geom. Dedicata 132 (2008) 1 MR2396906
12	A Pedroza, Seidel’s representation on the Hamiltonian group of a Cartesian product, Int. Math. Res. Not. 2008 (2008) MR2440331
13	A Pedroza, Hamiltonian loops on the symplectic one-point blow up, J. Symplectic Geom. 16 (2018) 839 MR3882174
14	L Polterovich, The geometry of the group of symplectic diffeomorphisms, Birkhäuser (2001) MR1826128
15	P Seidel, π₁ of symplectic automorphism groups and invertibles in quantum homology rings, Geom. Funct. Anal. 7 (1997) 1046 MR1487754
16	S Smale, Diffeomorphisms of the 2–sphere, Proc. Amer. Math. Soc. 10 (1959) 621 MR112149
17	A Weinstein, Cohomology of symplectomorphism groups and critical values of Hamiltonians, Math. Z. 201 (1989) 75 MR990190