Symplectomorphism groups and isotropic skeletons
نویسندگان
چکیده
منابع مشابه
Symplectomorphism groups and isotropic skeletons
The symplectomorphism group of a 2–dimensional surface is homotopy equivalent to the orbit of a filling system of curves. We give a generalization of this statement to dimension 4. The filling system of curves is replaced by a decomposition of the symplectic 4–manifold (M,ω) into a disjoint union of an isotropic 2–complex L and a disc bundle over a symplectic surface Σ which is Poincare dual to...
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We discuss the question of what quantummethods (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 symplectomorphism group of toric manifolds. This leads to a...
متن کاملar X iv : m at h . SG / 0 40 44 96 v 2 1 3 Ju l 2 00 4 Symplectomorphism groups and isotropic skeletons
The symplectomorphism group of a 2-dimensional surface S is homotopy equivalent to the orbit of a filling system of curves on S. We give a generalization of this statement to dimension 4. The filling system of curves is replaced by a decomposition of M into a disjoint union of an isotropic 2-complex L and a disc bundle over a symplectic surface Σ Poincare dual to a multiple of the form. We show...
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This paper studies groups of symplectomorphisms of ruled surfaces M for symplectic forms with varying cohomology class. This cohomology class is characterised by the ratio μ of the size of the base to that of the fiber. By considering appropriate spaces of almost complex structures, we investigate how the topological type of these groups changes as μ increases. If the base is a sphere, this cha...
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In dimension 4, due to non-existence of adequate tools, very little is known about the topology of groups of diffeomorphisms. For example, it is unknown if the group of compactly supported diffeomorphisms of R is connected. The situation is much better if one wants to study groups of symplectomorphisms. This is due to the existence of powerful tools, going by the name of “pseudo-holomorphic cur...
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ژورنال
عنوان ژورنال: Geometry & Topology
سال: 2005
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.2005.9.935