Continuous group actions on profinite spaces

For a profinite group, we construct a model structure on profinite spaces and profinite spectra with a continuous action. This yields descent spectral sequences for the homotopy groups of homotopy fixed point spaces and for stable homotopy groups of homotopy orbit spaces. Our main example is the Galois action on profinite étale topological types of varieties over a field. One motivation is to understand Grothendieck’s section conjecture in terms of homotopy fixed points.     

Time-resolved infrared spectroscopic study of reactive acyl intermediates relevant to cobalt-catalyzed carbonylations

Time-resolved infrared spectroscopic studies have been used to characterize the reactive intermediate CH3C(O)Co(CO)2PPh3 (ICo), which is relevant to the mechanism of the catalysis of alkene hydroformylation by the phosphine-modified cobalt carbonyls. Step-scan FTIR and (variable) single-frequency time-resolved infrared detection on the microsecond time scale were used to record the spectrum of ICo and to demonstrate that the principal photoproduct of the subsequent reaction of this species at PCO = 1 atm is the methyl cobalt complex CH3Co(CO)3PPh3 (MCo). At higher PCO the trapping of ICo with CO to re-form CH3C(O)Co(CO)3PPh3 (ACo) (rate = kCO[CO][ICo]) was shown to become competitive with the rate of acetyl-to-cobalt methyl migration to give MCo (rate = kM[ICo]). Activation parameters for the competing pathways in benzene were determined to be delta H++CO = 57 +/- 04 kJ mol-1, delta S++CO = -91 +/- 12 J mol-1 K-1 and delta H++M = 40 +/- 2 kJ mol-1, delta S++M = -19 +/- 5 J mol-1 K-1. The effects of varying the solvent on the competitive reactions of ICo were also explored, and the mechanistic implications of these results are discussed.     

Stable étale realization and étale cobordism

We show that there is a stable homotopy theory of profinite spaces and use it for two main applications. On the one hand we construct an étale topological realization of the stable A¹-homotopy theory of smooth schemes over a base field of arbitrary characteristic in analogy to the complex realization functor for fields of characteristic zero.On the other hand we get a natural setting for étale cohomology theories. In particular, we define and discuss an étale topological cobordism theory for schemes. It is equipped with an Atiyah-Hirzebruch spectral sequence starting from étale cohomology. Finally, we construct maps from algebraic to étale cobordism and discuss algebraic cobordism with finite coefficients over an algebraically closed field after inverting a Bott element.     

Versatile UHV system for combined far- and near-field magneto-optical microscopy of thin films

We have developed a UHV system for in situ studies of magnetic domains and magnetization reversal of thin films in the presence of external magnetic fields and at variable temperature. The system comprises a setup for magneto-optical Kerr effect measurements of magnetization curves, a Kerr-microscope for far-field magnetic-domain imaging, and a magneto-optical scanning near-field microscope in combination with a Sagnac interferometer (Sagnac-SNOM) for high-resolution imaging on a sub-μm scale. All components have successfully been tested, and the feasibility of studying ultrathin films has been demonstrated.