An infinite genus mapping class group and stable cohomology

We exhibit a finitely generated group \M whose rational homology is isomorphic to the rational stable homology of the mapping class group. It is defined as a mapping class group associated to a surface \su of infinite genus, and contains all the pure mapping class groups of compact surfaces of genus $g$ with $n$ boundary components, for any $g\geq 0$ and $n>0$. We construct a representation of \M into the restricted symplectic group ${\rm Sp_{res}}({\cal H}_r)$ of the real Hilbert space generated by the homology classes of non-separating circles on \su, which generalizes the classical symplectic representation of the mapping class groups. Moreover, we show that the first universal Chern class in H^2(\M,\Z) is the pull-back of the Pressley-Segal class on the restricted linear group ${\rm GL_{res}}({\cal H})$ via the inclusion ${\rm Sp_{res}}({\cal H}_r)\subset {\rm GL_{res}}({\cal H})$.Comment: 14p., 8 figures, to appear in Commun.Math.Phy

Equivariant geometric K-homology for compact Lie group actions

Let G be a compact Lie-group, X a compact G-CW-complex. We define equivariant geometric K-homology groups K^G_*(X), using an obvious equivariant version of the (M,E,f)-picture of Baum-Douglas for K-homology. We define explicit natural transformations to and from equivariant K-homology defined via KK-theory (the "official" equivariant K-homology groups) and show that these are isomorphism.Comment: 25 pages. v2: some mistakes corrected, more detail added, Michael Walter as author added. To appear in Abhandlungen aus dem Mathematischen Seminar der Universit\"at Hambur

Expansions of algebras and superalgebras and some applications

After reviewing the three well-known methods to obtain Lie algebras and superalgebras from given ones, namely, contractions, deformations and extensions, we describe a fourth method recently introduced, the expansion of Lie (super)algebras. Expanded (super)algebras have, in general, larger dimensions than the original algebra, but also include the Inonu-Wigner and generalized IW contractions as a particular case. As an example of a physical application of expansions, we discuss the relation between the possible underlying gauge symmetry of eleven-dimensional supergravity and the superalgebra osp(1|32).Comment: Invited lecture delivered at the 'Deformations and Contractions in Mathematics and Physics Workshop', 15-21 January 2006, Mathematisches Forschungsinstitut Oberwolfach, German

Felix Alexandrovich Berezin and his work

This is a survey of Berezin's work focused on three topics: representation theory, general concept of quantization, and supermathematics.Comment: LaTeX, 27 page

Luminescence spectra and kinetics of disordered solid solutions

We have studied both theoretically and experimentally the luminescence spectra and kinetics of crystalline, disordered solid solutions after pulsed excitation. First, we present the model calculations of the steady-state luminescence band shape caused by recombination of excitons localized in the wells of random potential induced by disorder. Classification of optically active tail states of the main exciton band into two groups is proposed. The majority of the states responsible for the optical absorption corresponds to the group of extended states belonging to the percolation cluster, whereas only a relatively small group of “radiative” states forms the steady-state luminescence band. The continuum percolation theory is applied to distinguish the “radiative” localized states, which are isolated in space and have no ways for nonradiative transitions along the tail states. It is found that the analysis of the exciton-phonon interaction gives the information about the character of the localization of excitons. We have shown that the model used describes quite well the experimental cw spectra of CdS(1−c)Sec and ZnSe(1−c)Tec solid solutions. Further, the experimental results are presented for the temporal evolution of the luminescence band. It is shown that the changes of band shape with time come from the interplay of population dynamics of extended states and spatially isolated “radiative” states. Finally, the measurements of the decay of the spectrally integrated luminescence intensity at long delay times are presented. It is shown that the observed temporal behavior can be described in terms of relaxation of separated pairs followed by subsequent exciton formation and radiative recombination. Electron tunneling processes are supposed to be responsible for the luminescence in the long-time limit at excitation below the exciton mobility edge. At excitation by photons with higher energies the diffusion of electrons can account for the observed behavior of the luminescence

A Historiometric Examination of Machiavellianism and a New Taxonomy of Leadership

Although researchers have extensively examined the relationship between charismatic leadership and Machiavellianism (Deluga, 2001; Gardner & Avolio, 1995; House & Howell, 1992), there has been a lack of investigation of Machiavellianism in relation to alternative forms of outstanding leadership. Thus, the purpose of this investigation was to examine the relationship between Machiavellianism and a new taxonomy of outstanding leadership comprised of charismatic, ideological, and pragmatic leaders. Using an historiometric approach, raters assessed Machiavellianism via the communications of 120 outstanding leaders in organizations across the domains of business, political, military, and religious institutions. Academic biographies were used to assess twelve general performance measures as well as twelve general controls and five communication specific controls. The results indicated that differing levels of Machiavellianism is evidenced across the differing leader types as well as differing leader orientation. Additionally, Machiavellianism appears negatively related to performance, though less so when type and orientation are taken into account.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline