34,272 research outputs found
Signatures of links in rational homology spheres
A theory of signatures for odd-dimensional links in rational homology spheres
is studied via their generalized Seifert surfaces. The jump functions of
signatures are shown invariant under appropriately generalized concordance and
a special care is given to accommodate 1-dimensional links with mutual linking.
Furthermore our concordance theory of links in rational homology spheres
remains highly nontrivial after factoring out the contribution from links in
integral homology spheres.Comment: 21 pages, 3 figures, to appear in Topology; references and pictures
update
Hartle-Hawking wave function and large-scale power suppression of CMB
In this presentation, we first describe the Hartle-Hawking wave function in
the Euclidean path integral approach. After we introduce perturbations to the
background instanton solution, following the formalism developed by
Halliwell-Hawking and Laflamme, one can obtain the scale-invariant power
spectrum for small-scales. We further emphasize that the Hartle-Hawking wave
function can explain the large-scale power suppression by choosing suitable
potential parameters, where this will be a possible window to confirm or
falsify models of quantum cosmology. Finally, we further comment on possible
future applications, e.g., Euclidean wormholes, which can result in distinct
signatures to the power spectrum.Comment: 5 pages, 1 figure; Proceedings of the 13th International Conference
on Gravitation, Astrophysics, and Cosmology & the 15th Italian-Korean
Symposium on Relativistic Astrophysics: A Joint Meeting. Talk on July 7,
2017, Seoul, Republic of Kore
Elliptic Operators and Higher Signatures
Building on the theory of elliptic operators, we give a unified treatment of
the following topics:
- the problem of homotopy invariance of Novikov's higher signatures on closed
manifolds;
- the problem of cut-and-paste invariance of Novikov's higher signatures on
closed manifolds;
- the problem of defining higher signatures on manifolds with boundary and
proving their homotopy invariance.Comment: 54 pages. Survey-article. Related papers can be retrieved from
http://www.mat.uniroma1.it/people/piazz
Shape description and matching using integral invariants on eccentricity transformed images
Matching occluded and noisy shapes is a problem frequently encountered in medical image analysis and more generally in computer vision. To keep track of changes inside the breast, for example, it is important for a computer aided detection system to establish correspondences between regions of interest. Shape transformations, computed both with integral invariants (II) and with geodesic distance, yield signatures that are invariant to isometric deformations, such as bending and articulations. Integral invariants describe the boundaries of planar shapes. However, they provide no information about where a particular feature lies on the boundary with regard to the overall shape structure. Conversely, eccentricity transforms (Ecc) can match shapes by signatures of geodesic distance histograms based on information from inside the shape; but they ignore the boundary information. We describe a method that combines the boundary signature of a shape obtained from II and structural information from the Ecc to yield results that improve on them separately
The L^2 signature of torus knots
We find a formula for the L2 signature of a (p,q) torus knot, which is the
integral of the omega-signatures over the unit circle. We then apply this to a
theorem of Cochran-Orr-Teichner to prove that the n-twisted doubles of the
unknot, for n not 0 or 2, are not slice. This is a new proof of the result
first proved by Casson and Gordon.Comment: 11 pages, Version 2 contains a note explaining that the main theorem
of the paper has already been proved in earlier work by Kirby and Melvi
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