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The Euler-Poincaré-Hopf theorem for flat connections in some transitive Lie algebroids

Jan Kubarski (2006)

Czechoslovak Mathematical Journal

This paper is a continuation of [19], [21], [22]. We study flat connections with isolated singularities in some transitive Lie algebroids for which either ℝ or s l ( 2 , ℝ ) or so ( 3 ) are isotropy Lie algebras. Under the assumption that the dimension of the isotropy Lie algebra is equal to n + 1 , where n is the dimension of the base manifold, we assign to any such isolated singularity a real number called an index. For ℝ -Lie algebroids, this index cannot be an integer. We prove the index theorem (the Euler-Poincaré-Hopf...

The Mumford conjecture

Geoffrey Powell (2004/2005)

Séminaire Bourbaki

The Mumford Conjecture asserts that the rational cohomology of the stable moduli space of Riemann surfaces is a polynomial algebra on the Mumford-Morita-Miller characteristic classes; this can be reformulated in terms of the classifying space B Γ ∞ derived from the mapping class groups. The conjecture admits a topological generalization, inspired by Tillmann’s theorem that B Γ ∞ admits an infinite loop space structure after applying Quillen’s plus construction. The text presents the proof by Madsen and...

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