Spin Structures on Kleinian Manifolds

We derive the topological obstruction to spin-Klein cobordism. This result has implications for signature change in general relativity, and for the $N=2$ superstring.Comment: 8 page

Some Remarks on Group Bundles and C*-dynamical systems

We introduce the notion of fibred action of a group bundle on a C(X)-algebra. By using such a notion, a characterization in terms of induced C*-bundles is given for C*-dynamical systems such that the relative commutant of the fixed-point algebra is minimal (i.e., it is generated by the centre of the given C*-algebra and the centre of the fixed-point algebra). A class of examples in the setting of the Cuntz algebra is given, and connections with superselection structures with nontrivial centre are discussed.Comment: 22 pages; to appear on Comm. Math. Phy

Fragmentation cross sections of O-16 between 0.9 and 200 GeV/nucleon

Inclusive cross sections for high energy interactions at 0.9, 2.3, 3.6, and 13.5 GeV/nucleon of O-16 with C, CR-39 (C12H18O7), CH2, Al, Cu, Ag, and Pb targets were measured. The total charge-changing cross sections and partial charge-changing cross sections for the production of fragments with charge Z = 6 and Z = 7 are compared to previous experiments at 60 and 200 GeV/nucleon. The contributions of Coulomb dissociation to the total cross sections are calculated. Using factorization rules the partial electromagnetic cross sections are separated from the nuclear components. Energy dependence of both components are investigated and discussed

Proton-induced fragmentation of carbon at energies below 100 MeV

Radiation effects caused by single cosmic ray particles have been studied for many years in radiobiological experiments for different biological objects and biological end-points. Additionally, single event effects in microelectronic devices have gained large interest. There are two fundamental mechanisms by which a single particle can cause radiation effects. On the one hand, a cosmic ray ion with high linear energy transfer can deposit a high dose along its path. On the other hand, in a nuclear collision, a high dose can be deposited by short range particles emitted from the target nucleus. In low earth orbits a large contribution to target fragmentation events originates from trapped protons which are encountered in the South Atlantic Anomaly. These protons have energies up to a few hundred MeV. We study the fragmentation of C, O and Si nuclei - the target nuclei of biological material and microelectronic devices - in nuclear collisions. Our aim is to measure production cross sections, energy spectra, emission directions and charge correlations of the emitted fragments. The present knowledge concerning these data is rather poor. M. Alurralde et al. have calculated cross sections and average energies of fragments produced from Si using the cascade-evaporation model. D.M. Ngo et al. have used the semiempirical cross section formula of Silberberg and Tsao to calculate fragment yields and the statistical model of Goldhaber to describe the reaction kinematics. Cross sections used in these models have uncertainties within a factor of two. Our data will help to test and improve existing models especially for energies below 300 MeV/nucleon. Charge correlations of fragments emitted in the same interaction are of particular importance, since high doses can be deposited if more than one heavy fragment with a short range is produced

The Γ^\hat{\Gamma}-genus and a regularization of an S1S^1-equivariant Euler class

We show that a new multiplicative genus, in the sense of Hirzebruch, can be obtained by generalizing a calculation due to Atiyah and Witten. We introduce this as the $\hat{\Gamma}$-genus, compute its value for some examples and highlight some of its interesting properties. We also indicate a connection with the study of multiple zeta values, which gives an algebraic interpretation for our proposed regularization procedure.Comment: 14 pages; version to appear in J. Phys.

Modular Invariance and Characteristic Numbers

We show that a general miraculous cancellation formula, the divisibility of certain characteristic numbers and some other topologiclal results are con- sequences of the modular invariance of elliptic operators on loop spaces. Previously we have shown that modular invariance also implies the rigidity of many elliptic operators on loop spaces.Comment: 14 page

Decoupling A and B model in open string theory -- Topological adventures in the world of tadpoles

In this paper we analyze the problem of tadpole cancellation in open topological strings. We prove that the inclusion of unorientable worldsheet diagrams guarantees a consistent decoupling of A and B model for open superstring amplitudes at all genera. This is proven by direct microscopic computation in Super Conformal Field Theory. For the B-model we explicitly calculate one loop amplitudes in terms of analytic Ray-Singer torsions of appropriate vector bundles and obtain that the decoupling corresponds to the cancellation of D-brane and orientifold charges. Local tadpole cancellation on the worldsheet then guarantees the decoupling at all loops. The holomorphic anomaly equations for open topological strings at one loop are also obtained and compared with the results of the Quillen formula

An algebraic proof of Bogomolov-Tian-Todorov theorem

We give a completely algebraic proof of the Bogomolov-Tian-Todorov theorem. More precisely, we shall prove that if X is a smooth projective variety with trivial canonical bundle defined over an algebraically closed field of characteristic 0, then the L-infinity algebra governing infinitesimal deformations of X is quasi-isomorphic to an abelian differential graded Lie algebra.Comment: 20 pages, amspro

Crossings, Motzkin paths and Moments

Kasraoui, Stanton and Zeng, and Kim, Stanton and Zeng introduced certain $q$-analogues of Laguerre and Charlier polynomials. The moments of these orthogonal polynomials have combinatorial models in terms of crossings in permutations and set partitions. The aim of this article is to prove simple formulas for the moments of the $q$-Laguerre and the $q$-Charlier polynomials, in the style of the Touchard-Riordan formula (which gives the moments of some $q$-Hermite polynomials, and also the distribution of crossings in matchings). Our method mainly consists in the enumeration of weighted Motzkin paths, which are naturally associated with the moments. Some steps are bijective, in particular we describe a decomposition of paths which generalises a previous construction of Penaud for the case of the Touchard-Riordan formula. There are also some non-bijective steps using basic hypergeometric series, and continued fractions or, alternatively, functional equations.Comment: 21 page