We formulate and describe a visual compactification of the Teichmüller space by Weil-Petersson geodesic rays emanating from a point X. We focus on analogies with Bers’s compactification: due to non-completeness, finite rays correspond to cusps, and such cusps are dense in the visual sphere. By analogy with a result of Kerckhoff and Thurston, we show the natural action of the mapping class group...

In a previous paper [K1] I have constructed a compactification KGLn of the general linear group GLn, which in many respects is analogous to the so called wonderful compactification of adjoint semisimple algebraic groups as studied by De Concini and Procesi. In particular there is an action of G = GLn × GLn on this compactification. In this paper we show how the space of global section of an arb...

1.2. Primer on Connections. Recall from Peng’s talk that a connection on P → X can be thought of in three ways: (1) As a field of horizontal subspaces: TpP = HpP⊕VpP , where V P = ker (π∗). (Note that Vp ∼= g, and Hp ∼= Tπ(p)X). (2) As a g-valued 1-form A ∈ ΩX (g) which is invariant w.r.t. the induced G-action on ΩX (g). (3) Given a representation of G on W , as a vector bundle connection on th...

A general formula is obtained for Yukawa couplings in compactification on Landau-Ginzburg orbifolds and corresponding Calabi-Yau spaces. Up to the kinetic term normalizations, this equates the classical Koszul ring structure with the LandauGinzburg orbifold chiral ring structure and the true superconformal field theory ring structure.

We study structures called d-frames which were developed by the last two authors for a bitopological treatment of Stone duality. These structures consist of a pair of frames thought of as the opens of two topologies, together with two relations which serve as abstractions of disjointness and covering of the space. With these relations, the topological separation axioms regularity and normality ...

Mathematical Morphology is a very efficient tool for image processing and analysis, based on non-linear local operators. In this paper mathematical morphology is applied to pattern recognition. The appropriate practical methods of morphological image processing are described, as well as its theoretical background. An example of an application of described methods to recognition of car number pl...

1. Differentiable Manifolds 2 2. Complex Manifolds 3 2.1. Riemann Surfaces of Genus One 4 2.2. Constructing Riemann Surfaces as Curves in P 6 2.3. Constructing Riemann Surfaces as Covers 9 2.4. Constructing Riemann Surfaces by Glueing 10 3. Topological Vector Bundles 11 3.1. The Tangent and Cotangent Bundles 13 3.2. Interlude: Categories, Complexes and Exact Sequences 14 3.3. Metrics on Vector ...

we characterize function spaces of rees matrixsemigroups. then we study these spaces by using the topologicaltensor product technique.

It is shown that a change in the signature of the space-time metric together with compactification of internal dimensions could occur in a six-dimensional cosmological model. We also show that this is due to interaction with Maxwell fields having support in the internal part of the space-time. PACS: 0.420.Gz,0.4.50+h

It is shown – using a FRW model with S 3 × S 6 as spatial sections and a positive cosmological constant – that classical signature change implies a new compactification mechanism. The internal scale factor is of the order Λ −1/2 , and the solutions are stable against small perturbatons. In the case of compactified S 6 , it is shown that the effective four-dimensional space-time metric has Loren...