Surgery on 3-manifolds with \mathbb{S} 1-actions

We study the topological structure of all 3-manifolds obtained by surgery along principal fibers of a closed orientable -manifold. As a consequence, we give alternative proofs of some classical results due to W. Heil and L. Moser. Moreover, we completely specify the Seifert invariants for the considered manifolds. Finally we classify the manifolds obtained by surgery along certain Seifert links and determine geometric presentations of their fundamental groups.Work performed under the auspices of C.N.R. (National Research Council) of Italy and partially supported by Ministero della Ricerca Scientifica e Tecnologica within the projects Geometria Reale e Complessa and Topologia.     

Families of Structures on Spherical Fibrations

Let SF(n) be the usual monoid of orientation- and base point-preserving self-equivalences of the n-sphere ${\mathbb{S}^n}$ n. If Y is a (right) SF(n)-space, one can construct a classifying space B(Y, SF(n), *)=B _n for ${\mathbb{S}^n}$ n-fibrations with Y-structure, by making use of the two-sided bar construction. Let k: B _n →BSF(n) be the forgetful map. A Y-structure on a spherical fibration corresponds to a lifting of the classifying map into B _n . Let K _i =K $\left( {{\mathbb{Z}_2 }} \right)$ , i) be the Eilenberg–Mac Lane space of type $\left( {{\mathbb{Z}_2 }} \right)$ , i). In this paper we study families of structures on a given spherical fibration. In particular, we construct a universal family of Y-structures, where Y=W _n is a space homotopy equivalent to ∏ _i≥1 K _i . Applying results due to Booth, Heath, Morgan and Piccinini, we prove that the universal family is a spherical fibration over the space map{B _n , B _n }×B _n . Furthermore, we point out the significance of this space for secondary characteristic classes. Finally, we calculate the cohomology of B _n .     

Sul grado delle rappresentazioni irriducibili del gruppo simmetrico

In this paper we use a result inK-theory to prove divisibility theorems of the degree of irreducible representations of the symmetric groups.     

Four-Manifolds With Surface Fundamental Groups

We study the homotopy type of closed connected topological -manifolds whose fundamental group is that of an aspherical surface . Then we use surgery theory to show that these manifolds are -cobordant to connected sums of simply-connected manifolds with an -bundle over .

     

On iterated Browder-Livesay invariants

Mathematical Notes - The Browder-Livesay invariants provide obstructions to the realization of elements of Wall groups by normal maps of closed manifolds. A generalization of the iterated...     

Nonlinear refractive indices of nonlinear liquids: wavelength dependence and influence of retarded response

We use liquid-filled capillary fibers with different core diameters to precisely characterize the nonlinear refractive index of the highly nonlinear liquids carbon disulfide, nitrobenzene, and toluene. We present measurements with two different femtosecond pump sources at wavelengths of 1032 and 1560 nm. The large nonlinearity of the liquids results from the retarded nonlinear optical response of the liquid molecules which includes a strong non-instantaneous contribution due to molecular reorientation. The nonlinear refractive index of the liquids is determined by fitting numerical simulations based on solving the generalized nonlinear Schrödinger equation including retarded response to the measured broadened output spectra. Our work is important for the novel field of near- and mid-IR supercontinuum generation in liquid-core optical fibers.     

Glassy properties of the relaxor ferroelectric strontium barium niobate at low temperatures

Relaxor ferroelectrics are known to show a low-temperature behaviour that quantitatively resembles the features of canonical glasses. In order to get a comprehensive characterisation of the responsible low-energy excitations, single crystals of strontium barium niobate were investigated below 10 K. The density of localised states was obtained from heat capacity, and their coupling to phonons from sound velocity and thermal conductivity. The presence of slowly relaxing systems could be estimated from heat release data, respectively.

In contrast with structural glasses, however, SBN and further relaxor ferroelectrics show an energy dependent density of states and an upper limit of the relaxation time spectrum. Considering these properties, which appear to be typical also for other glassy crystals, a modification of the standard tunneling model is proposed.