2,053 research outputs found
Morse-Novikov theory, Heegaard splittings and closed orbits of gradient flows
The works of Donaldson and Mark make the structure of the Seiberg-Witten
invariant of 3-manifolds clear. It corresponds to certain torsion type
invariants counting flow lines and closed orbits of a gradient flow of a
circle-valued Morse map on a 3-manifold. We study these invariants using the
Morse-Novikov theory and Heegaard splitting for sutured manifolds, and make
detailed computations for knot complements.Comment: 27 pages, 12 figure
AN EXTENSION OF BURAU REPRESENTATION OF THE BRAID GROUPS (Intelligence of Low-dimensional Topology)
Complements of hyperbolic knots of braid index four contain no closed embedded totally geodesic surfaces
AbstractWe prove that if F is a closed essential surface embedded in the complement of a knot K of braid index four, then at least one of the following holds: (1) F is meridionally compressible, (2) K is isotopic to a simple closed curve on F, (3) there is an essential annulus properly embedded in the closure of the component of S3−N(F) which does not contain K. We obtain a corollary that there are no closed embedded totally geodesic surfaces in the complements of hyperbolic knots of braid index four
Molecular Characterization of Polymethyl Acrylate in Dilute Solution (Special Issue on Polymer Chemistry, V)
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