14,870 research outputs found
Explicit concave fillings of contact three-manifolds
In this paper we give explicit, handle-by-handle constructions of concave
symplectic fillings of all closed, oriented contact 3-manifolds. These
constructions combine recent results of Giroux relating contact structures and
open book decompositions of 3-manifolds, earlier results of the author on
attaching 4-dimensional symplectic 2-handles along transverse links, and some
tricks with mapping class groups of compact surfaces with non-empty boundary.Comment: 15 pages. Accepted for publication in the Mathematical Proceedings of
the Cambridge Philosophical Society. Current version is identical to final
version submitted to the journal, differs from original version only in some
notation and minor editorial change
Reconstructing 4-manifolds from Morse 2-functions
Given a Morse 2-function , we give minimal conditions on the
fold curves and fibers so that and can be reconstructed from a
certain combinatorial diagram attached to . Additional remarks are made in
other dimensions.Comment: 13 pages, 10 figures. Replaced because the main theorem in the
original is false. The theorem has been corrected and counterexamples to the
original statement are give
Constructing symplectic forms on 4-manifolds which vanish on circles
Given a smooth, closed, oriented 4-manifold X and alpha in H_2(X,Z) such that
alpha.alpha > 0, a closed 2-form w is constructed, Poincare dual to alpha,
which is symplectic on the complement of a finite set of unknotted circles. The
number of circles, counted with sign, is given by d = (c_1(s)^2 -3sigma(X)
-2chi(X))/4, where s is a certain spin^C structure naturally associated to w.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol8/paper20.abs.htm
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