26,709 research outputs found
Links, two-handles, and four-manifolds
We show that only finitely many links in a closed 3-manifold share the same
complement, up to twists along discs and annuli. Using the same techniques, we
prove that by adding 2-handles on the same link we get only finitely many
smooth cobordisms between two given closed 3-manifolds.
As a consequence, there are finitely many smooth closed 4-manifolds
constructed from some Kirby diagram with bounded number of crossings, discs,
and strands, or from some Turaev special shadow with bounded number of
vertices. (These are the 4-dimensional analogues of Heegaard diagrams and
special spines for 3-manifolds.) We therefore get two filtrations on the set of
all smooth closed 4-manifolds with finite sets. The two filtrations are
equivalent after linear rescalings, and their cardinality grows at least as
n^{c*n}.Comment: 23 pages, 9 figures. Final versio
Hyperbolic three-manifolds that embed geodesically
We prove that every complete finite-volume hyperbolic 3-manifold that is
tessellated into right-angled regular polyhedra (dodecahedra or ideal
octahedra) embeds geodesically in a complete finite-volume connected orientable
hyperbolic 4-manifold , which is also tessellated into right-angled regular
polytopes (120-cells and ideal 24-cells). If is connected, then Vol() <
Vol(). This applies for instance to the Whitehead and the Borromean
links complements. As a consequence, the Borromean link complement bounds
geometrically a hyperbolic 4-manifold.Comment: 11 pages, 6 figures. Minor corrections from the previous version
Complexity of 3-manifolds
We give a summary of known results on Matveev's complexity of compact
3-manifolds. The only relevant new result is the classification of all closed
orientable irreducible 3-manifolds of complexity 10.Comment: 26 pages, 7 figures, minor correction
AdS/CFT Correspondence and Type 0 String Theory
We review some applications of Type 0 string theory in the context of the
AdS/CFT correspondence.Comment: 6 pages, LaTeX + JHEP.cls, talk presented at the TMR conference
``Quantum aspects of gauge theories, supersymmetry and unification'', Paris,
September 1-7, 199
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