Convexity properties of presymplectic moment maps

被引：10

作者：

Lin, Yi ^{[1
]}

Sjamaar, Reyer ^{[2
]}

机构：

[1] Georgia Southern Univ, Dept Math Sci, Statesboro, GA 30460 USA

[2] Cornell Univ, Dept Math, White Hall, Ithaca, NY 14853 USA

来源：

JOURNAL OF SYMPLECTIC GEOMETRY | 2019年 / 17卷 / 04期

基金：

中国国家自然科学基金;

关键词：

D O I：

10.4310/JSG.2019.v17.n4.a6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The convexity and Morse-theoretic properties of moment maps in symplectic geometry typically fail for presymplectic manifolds. We find a condition on presymplectic moment maps that prevents these failures. Our result applies for instance to Prato's quasifolds and to Hamiltonian actions on contact manifolds and cosymplectic manifolds.

引用

页码：1159 / 1200

页数：42

共 50 条

[31] Convexity criteria for set-valued maps
Sach, PH
Yen, ND
SET-VALUED ANALYSIS, 1997, 5 (01): : 37 - 45
[32] Convexity of multi-valued momentum maps
Giacobbe, A
GEOMETRIAE DEDICATA, 2005, 111 (01) : 1 - 22
[33] Convexity of Multi-valued Momentum Maps
Andrea Giacobbe
Geometriae Dedicata, 2005, 111 : 1 - 22
[34] Convexity Criteria for Set-Valued Maps
Pham Huu Sach
Nguyen Dong Yen
Set-Valued Analysis, 1997, 5 (1): : 37 - 45
[35] Moment Maps and Equivariant Volumes
Alberto DELLA VEDOVA
Roberto PAOLETTI
Acta Mathematica Sinica(English Series), 2007, 23 (12) : 2155 - 2188
[36] MOMENT MAPS AT THE QUANTUM LEVEL
LU, JH
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1993, 157 (02) : 389 - 404
[37] MOMENT METHODS FOR NONLINEAR MAPS
PUSCH, GD
NONLINEAR PROBLEMS IN ACCELERATOR PHYSICS, 1993, (131): : 51 - 76
[38] Dimensional reduction and moment maps
Nagatomo, Y
JOURNAL OF GEOMETRY AND PHYSICS, 2002, 41 (03) : 208 - 223
[39] Maps Preserving Moment Sequences
Carcamo, Javier
JOURNAL OF THEORETICAL PROBABILITY, 2017, 30 (01) : 212 - 232
[40] COURANT MORPHISMS AND MOMENT MAPS
Bursztyn, Henrique
Iglesias Ponte, David
Severa, Pavol
MATHEMATICAL RESEARCH LETTERS, 2009, 16 (2-3) : 215 - 232

← 1 2 3 4 5 →