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European Mathematical Society Publishing House
2024-03-29 11:22:36
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https://www.ems-ph.org/meta/jmeta-stream.php?jrn=PRIMS&vol=42&iss=3&update_since=2024-03-29
Publications of the Research Institute for Mathematical Sciences
Publ. Res. Inst. Math. Sci.
PRIMS
0034-5318
1663-4926
General
10.4171/PRIMS
http://www.ems-ph.org/doi/10.4171/PRIMS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© Research Institute for Mathematical Sciences, Kyoto University
42
2006
3
L2-Betti Numbers of Infinite Configuration Spaces
Sergio
Albeverio
Universität Bonn, BONN, GERMANY
Alexei
Daletskii
Nottingham Trent University, NOTTINGHAM, UNITED KINGDOM
Configuration space, infinite covering, de Rham cohomology, von Neumann algebra, Betti numbers, Poisson measure
The space ΓX of all locally finite configurations in a infinite covering X of a compact Riemannian manifold is considered. The de Rham complex of square-integrable differential forms over ΓX, equipped with the Poisson measure, and the corresponding de Rham cohomology and the spaces of harmonic forms are studied. A natural von Neumann algebra containing the projection onto the space of harmonic forms is constructed. Explicit formulae for the corresponding trace are obtained. A regularized index of the Dirac operator associated with the de Rham differential on the configuration space of an infinite covering is considered.
Global analysis, analysis on manifolds
Probability theory and stochastic processes
General
649
682
10.2977/prims/1166642153
http://www.ems-ph.org/doi/10.2977/prims/1166642153
Infinite Dimensionality of the Middle L2-cohomology on Non-compact Kähler Hyperbolic Manifolds
Bo-Yong
Chen
Tongji University, SHANGHAI, CHINA
We prove that the space of L2 harmonic forms of middle degree is infinite dimensional on any non-compact Kähler hyperbolic manifold.
Several complex variables and analytic spaces
General
683
689
10.2977/prims/1166642154
http://www.ems-ph.org/doi/10.2977/prims/1166642154
A Similarity Degree Characterization of Nuclear C∗-algebras
Gilles
Pisier
Texas A&M University, COLLEGE STATION, UNITED STATES
We show that a C∗-algebra A is nuclear iff there is a number α < 3 and a constant K such that, for any bounded homomorphism u : A → B(H), there is an isomorphism ξ : H → H satisfying ‖ξ−1‖ ‖ξ‖ ≤ K ‖u‖α and such that ξ−1 u(.)ξ is a ∗-homomorphism. In other words, an infinite dimensional A is nuclear iff its length (in the sense of our previous work on the Kadison similarity problem) is equal to 2.
Functional analysis
General
691
704
10.2977/prims/1166642155
http://www.ems-ph.org/doi/10.2977/prims/1166642155
On the Morawetz–Keel–Smith–Sogge Inequality for the Wave Equation on a Curved Background
Serge
Alinhac
Université Paris-Sud, ORSAY CX, FRANCE
Partial differential equations
General
705
720
10.2977/prims/1166642156
http://www.ems-ph.org/doi/10.2977/prims/1166642156
Belyi-Extending Maps and the Galois Action on Dessins d’Enfants
Melanie Matchett
Wood
Princeton University, PRINCETON, UNITED STATES
We study the absolute Galois group by looking for invariants and orbits of its faithful action on Grothendieck’s dessins d’enfants. We define a class of functions called Belyi-extending maps, which we use to construct new Galois invariants of dessins from previously known invariants. Belyi-extending maps are the source of “new-type” relations on the injection of the absolute Galois group into the Grothendieck–Teichmüller group. We make explicit how to get from a general Belyi-extending map to formula for its associated invariant which can be implemented in a computer algebra package. We give an example of a new invariant differing on two dessins which have the same values for the other readily computable invariants.
Algebraic geometry
Number theory
General
721
737
10.2977/prims/1166642157
http://www.ems-ph.org/doi/10.2977/prims/1166642157
Lie Tori—A Simple Characterization of Extended Affine Lie Algebras
Yoji
Yoshii
North Dakota State University, FARGO, UNITED STATES
We show the existence of a nonzero graded form on a Lie torus by the existence of a nonzero graded form on a structurable torus. This gives a simple characterization of the core of an extended affine Lie algebra (EALA). Namely, the core of any EALA is a Lie torus, and any centreless Lie torus is the centreless core of some EALA. We also show that a graded form on a Lie torus is unique up to scalars.
Nonassociative rings and algebras
General
739
762
10.2977/prims/1166642158
http://www.ems-ph.org/doi/10.2977/prims/1166642158
A General Seifert–Van Kampen Theorem for Algebraic Fundamental Groups
Jakob
Stix
Universität Bonn, BONN, GERMANY
A Seifert–Van Kampen theorem describes the fundamental group of a space in terms of the fundamental groups of the constituents of a covering and the configuration of connected components of the covering. Here we provide the combinatorial part of such a theorem for the most general sort of coverings. Thus a Seifert–Van Kampen theorem is reduced to a purely geometric statement of effective descent.
Algebraic geometry
Group theory and generalizations
General
763
786
10.2977/prims/1166642159
http://www.ems-ph.org/doi/10.2977/prims/1166642159
On the Occupation Time on the Half Line of Pinned Diffusion Processes
Yuko
Yano
Ochanomizu University, TOKYO, JAPAN
Brownian motion, arc-sine law, speed measure, Krein’s theory, Tauberian theorem
The aim of the present paper is to generalize Lévy’s result of the occupation e time on the half line of pinned Brownian motion for pinned diffusion processes. An asymptotic behavior of the distribution function at the origin of the occupation time Γ+(t) and limit theorem for the law of the fraction Γ+(t)/t when t → ∞ are studied. An expression of the distribution function by the Riemann–Liouville fractional integral for pinned skew Bessel diffusion processes is also obtained. Krein’s spectral theory and Tauberian theorem play important roles in the proofs.
Probability theory and stochastic processes
General
787
802
10.2977/prims/1166642160
http://www.ems-ph.org/doi/10.2977/prims/1166642160
Monodromy at Infinity and Fourier Transform II
Claude
Sabbah
Ecole Polytechnique, PALAISEAU CEDEX, FRANCE
Twistor D-module, Fourier–Laplace transform, specialization
For a regular twistor D-module and for a given function f, we compare the nearby cycles at f = ∞ and the nearby or vanishing cycles at τ = 0 for its partial Fourier–Laplace transform relative to the kernel e−τf.
Several complex variables and analytic spaces
Algebraic geometry
Ordinary differential equations
General
803
835
10.2977/prims/1166642161
http://www.ems-ph.org/doi/10.2977/prims/1166642161
Excursion Measure Away from an Exit Boundary of One-Dimensional Diffusion Processes
Kouji
Yano
Kyoto University, KYOTO, JAPAN
Diffusion process, excursion theory, Poisson point process, limit theorem, stable process, Krein’s spectral theory
A generalization of the excursion measure away from an exit boundary is defined for a one-dimensional diffusion process. It is constructed through the disintegration formula with respect to the lifetime. The counterpart of the Williams description, the disintegration formula with respect to the maximum, is also established. This generalized excursion measure is applied to explain and generalize the convergence theorem of Kasahara and Watanabe [8] in terms of the Poisson point fields, where the inverse local time processes of regular diffusion processes converge in the sense of probability law to some Lévy process, which is closely related to a diffusion process with an exit boundary.
Probability theory and stochastic processes
Ordinary differential equations
General
837
878
10.2977/prims/1166642162
http://www.ems-ph.org/doi/10.2977/prims/1166642162