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Groups of Lie type, vertex algebras, and modular moonshine
On the injectivity radius in Hofer's geometry
1. | Département de Mathématiques et de Statistique, Université de Montréal, C.P. 6128, Succ. Centre-ville, Montréal H3C 3J7, Québec, Canada |
2. | Centre de Recherches Mathématiques, Université de Montréal, C.P. 6128, Succ. Centre-ville, Montréal H3C 3J7, Québec, Canada |
References:
[1] |
D. Ebin and J. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. Math. (2), 92 (1970), 102-163.
doi: 10.2307/1970699. |
[2] |
M. Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math., 82 (1985), 307-347.
doi: 10.1007/BF01388806. |
[3] |
J. Kędra and D. McDuff, Homotopy properties of Hamiltonian group actions, Geom. Topol., 9 (2005), 121-162.
doi: 10.2140/gt.2005.9.121. |
[4] |
, M. Khanevsky and F. Zapolsky,, Private communication., ().
|
[5] |
F. Lalonde and D. McDuff, Hofer's $L^{\infty}$-geometry: Energy and stability of Hamiltonian flows. Part II, Invent. Math., 122 (1995), 35-69.
doi: 10.1007/BF01231438. |
[6] |
F. Lalonde and C. Pestieau, Stabilisation of symplectic inequalities and applications, in Northern California Symplectic Geometry Seminar, Amer. Math. Soc. Transl. Ser. 2, 196, Amer. Math. Soc., Providence, RI, 1999, 63-71. |
[7] |
L. Polterovich, Hofer's diameter and Lagrangian intersections, Internat. Math. Res. Notices, 4 (1998), 217-223.
doi: 10.1155/S1073792898000178. |
[8] |
Y. Savelyev, Virtual Morse theory on $\Omega\text{Ham}(M, \omega)$, J. Differ. Geom., 84 (2010), 409-425. |
[9] |
_____, Bott periodicity and stable quantum classes, Selecta Math. (N.S.), 19 (2013), 439-460. |
[10] |
_____, Quantum characteristic classes and the Hofer metric, Geom. Topol., 12 (2008), 2277-2326. |
[11] |
P. Seidel, $\pi_1$ of symplectic automorphism groups and invertibles in quantum homology rings, Geom. Funct. Anal., 7 (1997), 1046-1095.
doi: 10.1007/s000390050037. |
[12] |
Z. Shen, Lectures on Finsler Geometry, World Scientific Publishing Co., Singapore, 2001.
doi: 10.1142/9789812811622. |
show all references
References:
[1] |
D. Ebin and J. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. Math. (2), 92 (1970), 102-163.
doi: 10.2307/1970699. |
[2] |
M. Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math., 82 (1985), 307-347.
doi: 10.1007/BF01388806. |
[3] |
J. Kędra and D. McDuff, Homotopy properties of Hamiltonian group actions, Geom. Topol., 9 (2005), 121-162.
doi: 10.2140/gt.2005.9.121. |
[4] |
, M. Khanevsky and F. Zapolsky,, Private communication., ().
|
[5] |
F. Lalonde and D. McDuff, Hofer's $L^{\infty}$-geometry: Energy and stability of Hamiltonian flows. Part II, Invent. Math., 122 (1995), 35-69.
doi: 10.1007/BF01231438. |
[6] |
F. Lalonde and C. Pestieau, Stabilisation of symplectic inequalities and applications, in Northern California Symplectic Geometry Seminar, Amer. Math. Soc. Transl. Ser. 2, 196, Amer. Math. Soc., Providence, RI, 1999, 63-71. |
[7] |
L. Polterovich, Hofer's diameter and Lagrangian intersections, Internat. Math. Res. Notices, 4 (1998), 217-223.
doi: 10.1155/S1073792898000178. |
[8] |
Y. Savelyev, Virtual Morse theory on $\Omega\text{Ham}(M, \omega)$, J. Differ. Geom., 84 (2010), 409-425. |
[9] |
_____, Bott periodicity and stable quantum classes, Selecta Math. (N.S.), 19 (2013), 439-460. |
[10] |
_____, Quantum characteristic classes and the Hofer metric, Geom. Topol., 12 (2008), 2277-2326. |
[11] |
P. Seidel, $\pi_1$ of symplectic automorphism groups and invertibles in quantum homology rings, Geom. Funct. Anal., 7 (1997), 1046-1095.
doi: 10.1007/s000390050037. |
[12] |
Z. Shen, Lectures on Finsler Geometry, World Scientific Publishing Co., Singapore, 2001.
doi: 10.1142/9789812811622. |
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