We present two approaches to the study of the cohomology of moduli spaces of
curves. Together, they allow us to compute the rational cohomology of the
moduli space \Mbar_4 of stable complex curves of genus 4, with its Hodge
structure.Comment: 28 pages. Changes mainly of notational and expository nature. The
  published paper is available at http://www.springerlink.co

Bergström, Jonas