10,186 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
A Modified Hypersensitization Procedure for Eastman Kodak I-Z Spectroscopic Plates
Modified hypersensitization procedure for Eastman Kodak I-Z spectroscopic plate
Indefinite Morse 2-functions; broken fibrations and generalizations
A Morse 2-function is a generic smooth map from a smooth manifold to a
surface. In the absence of definite folds (in which case we say that the Morse
2-function is indefinite), these are natural generalizations of broken
(Lefschetz) fibrations. We prove existence and uniqueness results for
indefinite Morse 2-functions mapping to arbitrary compact, oriented surfaces.
"Uniqueness" means there is a set of moves which are sufficient to go between
two homotopic indefinite Morse 2-functions while remaining indefinite
throughout. We extend the existence and uniqueness results to indefinite, Morse
2-functions with connected fibers.Comment: 74 pages, 41 figures; further errors corrected, some exposition
added, other exposition improved, following referee's comment
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