Symplectic (-2)-spheres and the symplectomorphism group

2021 ◽  
Author(s):  
Jun Li ◽  
Tianjun Li ◽  
Weiwei Wu
Keyword(s):  
Symplectomorphism Group

scholarly journals The symplectomorphism group of a blow up

2007 ◽  
Vol 132 (1) ◽  
pp. 1-29 ◽  
Author(s):  
Dusa McDuff
Keyword(s):  
Blow Up ◽  
Symplectomorphism Group

ON THE TOPOLOGY OF THE EVALUATION MAP AND RATIONAL CURVES

2008 ◽  
Vol 19 (04) ◽  
pp. 369-385
Author(s):  
GERASIM KOKAREV
Keyword(s):  
Rational Curves ◽  
Vanishing Theorem ◽  
Topological Properties ◽  
Symplectomorphism Group

We explore a relationship between topological properties of the orbits of 2-cycles in the symplectomorphism group Symp(M) and the existence of rational curves in M. Under the absence of rational curves hypothesis, we show that the evaluation map vanishies on π2 and obtain a Gottlieb-type vanishing theorem for toroidal cycles in Symp(M).

A 2-Cocycle on a Symplectomorphism Group

2006 ◽  
Vol 6 (2) ◽  
pp. 307-315 ◽  
Author(s):  
R. Ismagilov ◽  
M. Losik ◽  
P. Michor
Keyword(s):  
Symplectomorphism Group

CHERN-SIMONS QUANTUM MECHANICS, SUPERSYMMETRY, AND SYMPLECTIC INVARIANTS

1991 ◽  
Vol 06 (03) ◽  
pp. 365-379 ◽  
Author(s):  
MATTHIAS BLAU
Keyword(s):  
Quantum Mechanics ◽  
Equivariant Cohomology ◽  
Explicit Calculation ◽  
Infinite Dimensions ◽  
Conformal Field ◽  
Mechanics Model ◽  
Topological Quantum ◽  
Symplectomorphism Group ◽  
Symplectic Invariants ◽  
Chern Simons

We explain the relation between supersymmetry and equivariant cohomology, combining recent investigations of Chern-Simons quantum mechanics and path integrals on coadjoint orbits. We then construct a supersymmetric (topological) quantum mechanics model whose partition function — probing the cohomology of the symplectomorphism group — yields a symplectic invariant introduced by Weinstein. We demonstrate by explicit calculation that this provides another example where the Duistermaat-Heckman theorem (exactness of the semi-classical approximation) appears to hold in infinite dimensions, and make some suggestions concerning its role in (conformal) field theory.

Sign in / Sign up

Export Citation Format

Share Document