Results 151 to 160 of about 1,106 (166)

Symplectomorphism group of $T^\ast (G_{\mathbb{C}} / B)$ and the braid group I: a homotopy equivalence for $G_{\mathbb{C}} = SL_3 (\mathbb{C})$

The Journal of Symplectic Geometry, 2014
For a semisimple Lie group $G_\mathbb{C}$ over $\mathbb{C}$, we study the homotopy type of the symplectomorphism group of the cotangent bundle of the flag variety and its relation to the braid group. We prove a homotopy equivalence between the two groups
Xin Jin
semanticscholar   +1 more source

Generating functions of symplectomorphisms

Functional Analysis and Its Applications, 1994
The author suggests a construction which allows him to replace the infinite-dimensional loop space by the finite-dimensional space of closed polygons in the Conley-Zehnder's proof of Arnol'd's problem on fixed points of symplectic diffeomorphisms of tori.
openaire   +2 more sources

The group of symplectomorphisms

2017
This chapter discusses the basic properties of the group of symplectomorphisms of a compact connected symplectic manifold and its subgroup of Hamiltonian symplectomorphisms. It begins by showing that the group of symplectomorphisms is locally path-connected and then moves on to the flux homomorphism.
Dusa McDuff, Dietmar Salamon
openaire   +1 more source

Fixed points of non-Hamiltonian symplectomorphisms

Journal of Geometric Analysis, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

The symplectomorphism group of a blow up

, 2006
We study the relation between the symplectomorphism group Symp M of a closed connected symplectic manifold M and the symplectomorphism and diffeomorphism groups Symp $$\widetilde{M}$$ and Diff $$\widetilde{M}$$ of its one point blow up $$\widetilde{M}$$ .
D. Mcduff
semanticscholar   +1 more source

The Group of Hamiltonian Symplectomorphisms

2011
Symplectic diffeomorphisms, or symplectomorphisms as they are often called, are the “canonical transformations” which have been known and used by physicists for a long time. They generalize the linear (and affine) symplectic mappings we have been using so far. A basic reference for this chapter is Polterovich [133].
openaire   +1 more source

The Homotopy Lie Algebra of Symplectomorphism Groups of 3-Fold Blowups of (S2×S2,σstd⊕σstd)

The Michigan mathematical journal, 2019
Sílvia Anjos, Sinan Eden
semanticscholar   +2 more sources

Symplectomorphism Groups and Quantum Cohomology

2007
We discuss the question of what quantum methods (J-holomorphic curves and quantum homology) can tell us about the symplectomorphism group and its compact subgroups. After describing the rather complete information we now have about the case of the product of two 2-spheres, we describe some recent results of McDuff-Tolman concerning the ...
openaire   +1 more source

The primitive function of an exact symplectomorphism

Nonlinearity, 2000
Summary: Let \(\mathcal O\) be the zero-section of the cotangent bundle \(T^*\mathcal M\) of a real analytic manifold \(\mathcal M\). Let \(F: (T^*\mathcal M,\mathcal O)\to(T^*\mathcal M,\mathcal O)\) be a real analytic local diffeomorphism preserving the canonical symplectic form \(\omega = d\alpha\) of \(T^*\mathcal M\), where \(\alpha\) denotes the ...
openaire   +1 more source

Conjugate points on the symplectomorphism group

Annals of Global Analysis and Geometry, 2015
J. Benn
semanticscholar   +2 more sources