Quasi-morphisms and Symplectic Quasi-states for Convex Symplectic Manifolds

被引：13

作者：

Lanzat, Sergei ^{[1
]}

机构：

[1] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2013年 / 2013卷 / 23期

关键词：

HAMILTONIAN-DYNAMICS; SPECTRAL INVARIANTS; POISSON BRACKETS; FLOER THEORY; DIFFEOMORPHISMS; TOPOLOGY; RIGIDITY; HOMOLOGY; GEOMETRY; ENERGY;

D O I：

10.1093/imrn/rns205

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We use quantum and Floer homology to construct (partial) quasi-morphisms on the universal cover (Ham) over tilde (c)(M, omega) of the group of compactly supported Hamiltonian diffeomorphisms for a certain class of nonclosed strongly semi-positive symplectic manifolds (M, omega). This leads to a construction of (partial) symplectic quasi-states on the space C-cc(M) of continuous functions on M that are constant near infinity. The work extends the results by Entov and Polterovich which apply in the closed case.

引用

页码：5321 / 5365

页数：45

共 50 条

[1] Quasi-morphisms and quasi-states in symplectic topology
Entov, Michael
[J]. PROCEEDINGS OF THE INTERNATIONAL CONGRESS OF MATHEMATICIANS (ICM 2014), VOL II, 2014, : 1147 - 1171
[2] SYMPLECTIC REDUCTION OF QUASI-MORPHISMS AND QUASI-STATES
Borman, Matthew Strom
[J]. JOURNAL OF SYMPLECTIC GEOMETRY, 2012, 10 (02) : 225 - 246
[3] Quasi-States, Quasi-Morphisms, and the Moment Map
Borman, Matthew Strom
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2013, 2013 (11) : 2497 - 2533
[4] Calabi quasi-morphisms for some non-monotone symplectic manifolds
Ostrover, Yaron
[J]. ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2006, 6 : 405 - 434
[5] Quasi-states and symplectic intersections
Entov, M
Polterovich, L
[J]. COMMENTARII MATHEMATICI HELVETICI, 2006, 81 (01) : 75 - 99
[6] POISSON BRACKETS, QUASI-STATES AND SYMPLECTIC INTEGRATORS
Entov, Michael
Polterovich, Leonid
Rosen, Daniel
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2010, 28 (04) : 1455 - 1468
[7] A COMPARISON OF SYMPLECTIC HOMOGENIZATION AND CALABI QUASI-STATES
Monzner, Alexandra
Zapolsky, Frol
[J]. JOURNAL OF TOPOLOGY AND ANALYSIS, 2011, 3 (03) : 243 - 263
[8] PY-CALABI QUASI-MORPHISMS AND QUASI-STATES ON ORIENTABLE SURFACES OF HIGHER GENUS
Rosenberg, Maor
[J]. ISRAEL JOURNAL OF MATHEMATICS, 2010, 180 (01) : 163 - 188
[9] Py-calabi quasi-morphisms and quasi-states on orientable surfaces of higher genus
Maor Rosenberg
[J]. Israel Journal of Mathematics, 2010, 180 : 163 - 188
[10] Symplectic quasi-states and semi-simplicity of quantum homology
Entov, Michael
Polterovich, Leonid
[J]. TORIC TOPOLOGY, 2008, 460 : 47 - +

← 1 2 3 4 5 →