Multiple period integrals and cohomology

This work gives a version of the Eichler-Shimura isomorphism with a non-abelian $H^1$ in group cohomology. Manin has given a map from vectors of cusp forms to a noncommutative cohomology set by means of iterated integrals. We show Manin's map is injective but far from surjective. By extending Manin's map we are able to construct a bijective map and remarkably this establishes the existence of a non-abelian version of the Eichler-Shimura map

Colour Gradients in the Optical and Near-IR

For many years broadband colours have been used to obtain insight into the contents of galaxies, in particular to estimate stellar and dust content. Broadband colours are easy to obtain for large samples of objects, making them ideal for statistical studies. In this paper I use the radial distribution of the colours in galaxies, which gives more insight into the local processes driving the global colour differences than integrated colours. Almost all galaxies in my sample of 86 face-on galaxies become systematically bluer with increasing radius. The radial photometry is compared to new dust extinction models and stellar population synthesis models. This comparison shows that the colour gradients in face-on galaxies are best explained by age and metallicity gradients in the stellar populations and that dust reddening plays a minor role. The colour gradients imply $M/L$ gradients, making the `missing light' problem as derived from rotation curve fitting even worse.Comment: 5 pages TeX file, 5 PostScript figures using epsf.sty To appear in proceedings of the ESO Workshop on "Spiral Galaxies in the Near-IR", eds.: D. Minniti, H.-W. Rix A gzipped PostScript version with figures in text can be obtained at http://star-www.dur.ac.uk/~rdejong/papers.htm