Divisors in the moduli spaces of curves
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In this mostly expository paper we review several known results about the cohomology of moduli spaces of smooth and stable curves, focusing in particular on low degree cohomology. We also give a new proof of Harer's theorem describing the second cohomology group of the moduli space of smooth n-pointed curves of given genus
18 pages, 1 figure; written for Surveys in Differential Geometry. Minor mistakes corrected, references added
18 pages, 1 figure; written for Surveys in Differential Geometry. Minor mistakes corrected, references added