2,835 research outputs found
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
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
Why is Our Food Making Us Sick?
The crowded, stressful conditions on factory farms are not only horrific for animals; they can have devastating implications for human healt
A Killer Show
An excerpt from the forthcoming book Death at SeaWorld takes a hard-hitting look at the marine mammal display industry in the wake of the February 2010 trainer death at SeaWorld Orlando
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