Mapping the surgery exact sequence for topological manifolds to analysis

In this paper we prove the existence of a natural mapping from the surgery exact sequence for topological manifolds to the analytic surgery exact sequence of N. Higson and J. Roe. This generalizes the fundamental result of Higson and Roe, but in the treatment given by Piazza and Schick, from smooth manifolds to topological manifolds. Crucial to our treatment is the Lipschitz signature operator of Teleman. We also give a generalization to the equivariant setting of the product defined by Siegel in his Ph.D. thesis. Geometric applications are given to stability results for rho classes. We also obtain a proof of the APS delocalised index theorem on odd dimensional manifolds, both for the spin Dirac operator and the signature operator, thus extending to odd dimensions the results of Piazza and Schick. Consequently, we are able to discuss the mapping of the surgery sequence in all dimensions.Comment: 26 pages, accepted in "Journal of Topology and Analysis

Singular spaces, groupoids and metrics of positive scalar curvature

We define and study, under suitable assumptions, the fundamental class, the index class and the rho class of a spin Dirac operator on the regular part of a spin stratified pseudomanifold. More singular structures, such as singular foliations, are also treated. We employ groupoid techniques in a crucial way; however, an effort has been made in order to make this article accessible to readers with only a minimal knowledge of groupoids. Finally, whenever appropriate, a comparison between classical microlocal methods and groupoids methods has been provided.Comment: 50 page

Mapping analytic surgery to homology, higher rho numbers and metrics of positive scalar curvature

Let $\Gamma$ be a f.g. discrete group and let $\tilde M$ be a Galois $\Gamma$-covering of a smooth closed manifold $M$. Let $S_*^\Gamma(\tilde{M})$ be the analytic structure group, appearing in the Higson-Roe analytic surgery sequence $\to S_*^\Gamma(\tilde M)\to K_*(M)\to K_*(C_r^*\Gamma)\to$. We prove that for an arbitrary discrete group $\Gamma$ it is possible to map the whole Higson-Roe sequence to the long exact sequence of even/odd-graded noncommutative de Rham homology $\to H_{[*-1]}(\mathcal{A}\Gamma)\to H^{del}_{[*-1]}(\mathcal{A}\Gamma)\to H^{e}_{[*]}(\mathcal{A}\Gamma)\to$, with $\mathcal{A}\Gamma$ a dense homomorphically closed subalgebra of $C^*_r\Gamma$. Here, $H_{*}^{del}(\mathcal{A}\Gamma)$ is the delocalized homology and $H_{*}^{e}(\mathcal{A}\Gamma)$ is the homology localized at the identity element. Then, under additional assumptions on $\Gamma$, we prove the existence of a pairing between $HC^*_{del}(\mathbb{C}\Gamma)$, the delocalized part of the cyclic cohomology of $\mathbb{C}\Gamma$, and $H^{del}_{*-1}(\mathcal{A}\Gamma)$. This, in particular, gives a pairing between $S^\Gamma_*(\tilde M)$ and $HC^{*-1}_{del}(\mathbb{C}\Gamma)$. We also prove the existence of a pairing between $S^\Gamma_*(\tilde M)$ and the relative cohomology $H^{[*-1]}(M\to B\Gamma)$. Both these parings are compatible with known pairings associated with the other terms in the Higson-Roe sequence. In particular, we define higher rho numbers associated to the rho class $\rho(\tilde D)\in S_*^\Gamma(\tilde M)$ of an invertible $\Gamma$-equivariant Dirac type operator on $\tilde M$. Finally, we provide a precise study for the behavior of all previous K-theoretic and homological objects and of the higher rho numbers under the action of the diffeomorphism group of $M$. Then, we establish new results on the moduli space of metrics of positive scalar curvature when $M$ is spin.Comment: 103 pages. Changes from the first version: the title has been modified; imprecisions have been corrected; more details are given; several new sections with many geometric applications have been adde

Ressenyes

Index de les obres ressenyades: Carme MOLINERO, La captación de las masas. Política social y propaganda en el régimen franquist

Laser-Assisted Mass Spectrometry

The wide range of uses for laser-assisted mass spectrometry is presented and illustrated with examples. In contrast to the practical aspects of these methods, knowledge about desorption and ion formation mechanisms in laser MS is lagging behind. Our group's efforts to unravel these mechanisms are also discussed

Advances in Surface Analysis and Mass Spectrometry Using Laser Desorption Methods

Laser desorption methods have profoundly influenced surface analysis and mass spectrometry. They provide snapshots of surface processes and allow detection of minute quantities of surface adsorbates. They allow the intact vaporization of polar, nonvolatile, high molecular weight, and thermally labile compounds that would otherwise be inaccessible to gas-phase studies. This contribution presents some recent advances in the field of laser desorption from surfaces, describes the experimental realization of a two-step laser mass spectrometer, highlights new insights into the mechanism of laser-induced thermal desorption, and illustrates the practical usefulness of the methodology with selected analytical examples

Genealogia dell’attore ideale: note sull’estetica drammaturgica schilleriana e le sue fonti

An important chapter in Schiller's speculation on the concept of nature regards the verisimilitude of the artifice, and particularly of the theatrical representation. In "Kallias-Briefe", the ideal of a full stylistic maturity that can be practised in the treatment of the matter, finds a privileged expression in the figure of the actor and in his capacity of transferring his subjectivity to the interpretation of the role. The author of the essay further demonstrates how these issues are linked to the broader debate on the art of mime that interests the whole European theatrical culture in the second half of the 18th Century, which, in Germany, turns around the figures of Ekhof, Schröder and Iffland