1,721,017 research outputs found
Analytic formulas for the topological degree of non-smooth mappings: The odd-dimensional case
No full textAbstractThe notion of topological degree is studied for mappings from the boundary of a relatively compact strictly pseudo-convex domain in a Stein manifold into a manifold in terms of index theory of Toeplitz operators on the Hardy space. The index formalism of non-commutative geometry is used to derive analytic integral formulas for the index of a Toeplitz operator with Hölder continuous symbol. The index formula gives an analytic formula for the degree of a Hölder continuous mapping from the boundary of a strictly pseudo-convex domain
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Mini-Workshop: Operator Spaces and Noncommutative Geometry in Interaction
Full text linkIn recent years, operator space theory has made remarkable appearances in noncommutative geometry, notably in the study of -algebras of real reductive groups and the unbounded picture of Kasparov theory. In both these developments, a central rôle is played by operator modules and the Haagerup tensor product. This workshop brought together experts in the aforementioned fields to deepen this interaction
Noncommutative deformation of the Ward metric
No full textThe moduli-space metric in the static non-Abelian charge-two sector of the Moyal-deformed CP1 sigma model in 1+2 dimensions is analyzed. After recalling the commutative results of Ward and Ruback and the ?-regularized construction of the noncommutative Kahler potential due to the second author, explicit expressions and asymptotics for it are presented and discussed in different regions of the moduli space. Along two curves in the moduli space the potential can be calculated analytically. In the region of solitons known as "ring-like", perturbation theory is used. In the region of "lump-like" solitons, both perturbation theory and the z -function approach are employed. While the strong noncommutativity limit is smooth and under control, the commutative limit in the two-lump region remains a semiclassical challenge
Noncommutative deformation of the Ward metric
No full textThe moduli-space metric in the static non-Abelian charge-two sector of the Moyal-deformed CP1 sigma model in 1+2 dimensions is analyzed. After recalling the commutative results of Ward and Ruback and the ζ-regularized construction of the noncommutative Kahler potential due to the second author, explicit expressions and asymptotics for it are presented and discussed in different regions of the moduli space. Along two curves in the moduli space the potential can be calculated analytically. In the region of solitons known as "ring-like", perturbation theory is used. In the region of "lump-like" solitons, both perturbation theory and the ζ-function approach are employed. While the strong noncommutativity limit is smooth and under control, the commutative limit in the two-lump region remains a semiclassical challenge
Index formulas and charge deficiencies on the Landau levels
No full textThe notion of charge deficiency by Avron et al. [“Charge deficiency, charge transport and comparison of dimensions,” Commun. Math. Phys. 159, 399 (1994) ] is studied from the view of K-theory of operator algebras and is applied to the Landau levels in \R^{2n}. We calculate the charge deficiencies at the higher Landau levels in \R^{2n} by means of an Atiyah–Singer-type index theorem
Analytic formulas for topological degree of non-smooth mappings: the even-dimensional case
No full textTopological degrees of continuous mappings between oriented manifolds of even dimension are studied in terms of index theory of pseudo-differential operators. The index formalism of non-commutative geometry is used to derive analytic integral formulas for the index of a 0th order pseudo-differential operator twisted by a Holder continuous complex vector bundle. The index formula gives an analytic formula for the degree of a Holder continuous mapping between even-dimensional oriented manifolds. The paper is an independent continuation of the paper Analytic formulas for topological degree of non-smooth mappings: the odd-dimensional case
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Index theory in geometry and physics
No full textThis thesis contains three papers in the area of index theory and its applications in geometry and mathematical physics. These papers deal with the problems of calculating the charge deficiency on the Landau levels and that of finding explicit analytic formulas for mapping degrees of Hölder continuous mappings. The first paper deals with charge deficiencies on the Landau levels for non-interacting particles in R^2 under a constant magnetic field, or equivalently, one particle moving in a constant magnetic field in even-dimensional Euclidian space. The K-homology class that the charge of a Landau level defines is calculated in two steps. The first step is to show that the charge deficiencies are the same on every particular Landau level. The second step is to show that the lowest Landau level, which is equivalent to the Fock space, defines the same class as the K-homology class on the sphere defined by the Toeplitz operators in the Bergman space of the unit ball. The second and third paper uses regularization of index formulas in cyclic cohomology to produce analytic formulas for the degree of Hölder continuous mappings. In the second paper Toeplitz operators and Henkin-Ramirez kernels are used to find analytic formulas for the degree of a function from the boundary a relatively compact strictly pseudo-convex domain in a Stein manifold to a compact connected oriented manifold. In the third paper analytic formulas for Hölder continuous mappings between general even-dimensional manifolds are produced using a pseudo-differential operator associated with the signature operator
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