Competition in European Telecom Markets

In recent years, the European telecommunications market has witnessed major developments, with rapid expansion in access to telecommunications networks and a surge in the number of available services and applications. While many factors have contributed to the transformation of the telecommunications industry, competition has played a key role in driving telecom players to invest in new technologies, to innovate and to offer new services. Increased competitive pressure is being felt across all market segments, even though significant differences remain across services and countries. Broadband roll-out has allowed operators to offer multiple-play services, thereby transforming traditional segment boundaries and competitive market structures.competition; access; convergence; multiple-play; fixed telephony; mobile services; broadband; VoIP; MVNO

Symplectic Geometry of Supersymmetry and Nonlinear Sigma Model

Recently it has been argued, that Poincar\'{e} supersymmetric field theories admit an underlying loop space hamiltonian (symplectic) structure. Here shall establish this at the level of a general $N=1$ supermultiplet. In particular, we advocate the use of a superloop space and explain the necessity of using nonconventional auxiliary fields. As an example we consider the nonlinear $\sigma$-model. Due to the quartic fermionic term, we conclude that the use of superloop space variables is necessary for the action to have a hamiltonian loop space interpretation.Comment: 9 pages, UU-ITP 30/9

The B model as a twisted spinning particle

The B-twisted topological sigma model coupled to topological gravity is supposed to be described by an ordinary field theory: a type of holomorphic Chern-Simons theory for the open string, and the Kodaira-Spencer theory for the closed string. We show that the B model can be represented as a PARTICLE theory, obtained by reducing the sigma model to one dimension, and replacing the coupling to topological gravity by a coupling to a twisted one-dimensional supergravity. The particle can be defined on ANY Kahler manifold--it does not require the Calabi-Yau condition--so it may provide a more generalized setting for the B model than the topological sigma model. The one-loop partition function of the particle can be written in terms of the Ray-Singer torsion of the manifold, and agrees with that of the original B model. After showing how to deform the Kahler and complex structures in the particle, we prove the independence of this partition function on the Kahler structure, and investigate the origin of the holomorphic anomaly. To define other amplitudes, one needs to introduce interactions into the particle. The particle will then define a field theory, which may or may not be the Chern-Simons or Kodaira-Spencer theories.Comment: 25/17 Pages big/little (LaTeX), TAUP-2192-94, CERN-TH.7402/9

Determinant bundles, boundaries, and surgery

In this note we specialize and illustrate the ideas developed in the paper math.DG/0201112 of the first author ("Index theory, eta forms, and Deligne cohomology ") in the case of the determinant line bundle. We discuss the surgery formula in the adiabatic limit using the adiabatic decomposition formula of the zeta regularized determinant of the Dirac Laplacian obtained by the second author and K. Wojciechowski.Comment: 23 page

Cohomological Partition Functions for a Class of Bosonic Theories

We argue, that for a general class of nontrivial bosonic theories the path integral can be related to an equivariant generalization of conventional characteristic classes.Comment: 9 pages; standard LATEX fil

Equivariant Kaehler Geometry and Localization in the G/G Model

We analyze in detail the equivariant supersymmetry of the $G/G$ model. In spite of the fact that this supersymmetry does not model the infinitesimal action of the group of gauge transformations, localization can be established by standard arguments. The theory localizes onto reducible connections and a careful evaluation of the fixed point contributions leads to an alternative derivation of the Verlinde formula for the $G_{k}$ WZW model. We show that the supersymmetry of the $G/G$ model can be regarded as an infinite dimensional realization of Bismut's theory of equivariant Bott-Chern currents on K\"ahler manifolds, thus providing a convenient cohomological setting for understanding the Verlinde formula. We also show that the supersymmetry is related to a non-linear generalization (q-deformation) of the ordinary moment map of symplectic geometry in which a representation of the Lie algebra of a group $G$ is replaced by a representation of its group algebra with commutator $[g,h] = gh-hg$. In the large $k$ limit it reduces to the ordinary moment map of two-dimensional gauge theories.Comment: LaTex file, 40 A4 pages, IC/94/108 and ENSLAPP-L-469/9

Gravitational Chern-Simons and the adiabatic limit

We compute the gravitational Chern-Simons term explicitly for an adiabatic family of metrics using standard methods in general relativity. We use the fact that our base three-manifold is a quasi-regular K-contact manifold heavily in this computation. Our key observation is that this geometric assumption corresponds exactly to a Kaluza-Klein Ansatz for the metric tensor on our three manifold, which allows us to translate our problem into the language of general relativity. Similar computations have been performed in a paper of Guralnik, Iorio, Jackiw and Pi (2003), although not in the adiabatic context.Comment: 17 page

Axioms for higher torsion invariants of smooth bundles

We explain the relationship between various characteristic classes for smooth manifold bundles known as ``higher torsion'' classes. We isolate two fundamental properties that these cohomology classes may or may not have: additivity and transfer. We show that higher Franz-Reidemeister torsion and higher Miller-Morita-Mumford classes satisfy these axioms. Conversely, any characteristic class of smooth bundles satisfying the two axioms must be a linear combination of these two examples. We also show how higher torsion invariants can be computed using only the axioms. Finally, we explain the conjectured formula of S. Goette relating higher analytic torsion classes and higher Franz-Reidemeister torsion.Comment: 24 pages, 0 figure