Measuring and calibrating Galactic synchrotron emission

Our position inside the Galaxy requires all-sky surveys to reveal its large-scale properties. The zero-level calibration of all-sky surveys differs from standard 'relative' measurements, where a source is measured in respect to its surroundings. All-sky surveys aim to include emission structures of all angular scales exceeding their angular resolution including isotropic emission components. Synchrotron radiation is the dominating emission process in the Galaxy up to frequencies of a few GHz, where numerous ground based surveys of the total intensity up to 1.4 GHz exist. Its polarization properties were just recently mapped for the entire sky at 1.4 GHz. All-sky total intensity and linear polarization maps from WMAP for frequencies of 23 GHz and higher became available and complement existing sky maps. Galactic plane surveys have higher angular resolution using large single-dish or synthesis telescopes. Polarized diffuse emission shows structures with no relation to total intensity emission resulting from Faraday rotation effects in the interstellar medium. The interpretation of these polarization structures critically depends on a correct setting of the absolute zero-level in Stokes U and Q.Comment: 10 pages, 8 figures. To be published in "Cosmic Magnetic Fields: From Planets, to Stars and Galaxies", K.G. Strassmeier, A.G. Kosovichev & J.E. Beckman, eds., Proc. IAU Symp. 259, CU

Novikov-Shubin invariants for arbitrary group actions and their positivity

We extend the notion of Novikov-Shubin invariant for free G-CW-complexes of finite type to spaces with arbitrary G-actions and prove some statements about their positivity. In particular we apply this to classifying spaces of discrete groups.Comment: 18 pages, metadata change

Commuting homotopy limits and smash products

In general the processes of taking a homotopy inverse limit of a diagram of spectra and smashing spectra with a fixed space do not commute. In this paper we investigate under what additional assumptions these two processes do commute. In fact we deal with an equivariant generalization which involves spectra and smash products over the orbit category of a discrete group. Such a situation naturally occurs if one studies the equivariant homology theory associated to topological cyclic homology. The main theorem of this paper will play a role in the generalization of the results obtained by Boekstedt, Hsiang and Madsen about the algebraic K-theory Novikov Conjecture to the assembly map for the family of virtually cyclic subgroups.Comment: 23 page

Algebraic K-theory of group rings and the cyclotomic trace map

We prove that the Farrell-Jones assembly map for connective algebraic K-theory is rationally injective, under mild homological finiteness conditions on the group and assuming that a weak version of the Leopoldt-Schneider conjecture holds for cyclotomic fields. This generalizes a result of B\"okstedt, Hsiang, and Madsen, and leads to a concrete description of a large direct summand of $K_n(\mathbb{Z}[G])\otimes_{\mathbb{Z}}\mathbb{Q}$ in terms of group homology. In many cases the number theoretic conjectures are true, so we obtain rational injectivity results about assembly maps, in particular for Whitehead groups, under homological finiteness assumptions on the group only. The proof uses the cyclotomic trace map to topological cyclic homology, B\"okstedt-Hsiang-Madsen's functor C, and new general isomorphism and injectivity results about the assembly maps for topological Hochschild homology and C.Comment: To appear in Advances in Mathematics. 77 page