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On Gromov's macroscopic dimension

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Alexander Dranishnikov
U Florida/MPI
Mon, 2010-07-05 15:00 - 16:00
MPIM Lecture Hall
Parent event: 
Topics in Topology

Gromov introduced the notion of macroscopic dimension to study closed manifolds with positive scalar curvature (PSC). In the talk we will discuss two his conjectures on the subject: I. If a closed $n$-manifold $M$ admits a PSC metric, then the macroscopic dimension of its universal cover is less than $n-1$. II. If the universal cover of a closed $n$-manifold $M$ has the macroscopic dimension less than $n$, then the image of the fundamental class under a map classifying the universal cover is trivial, $f_*([M])=0$, in the rational homology of the classifying space $H_*(B\pi)$.

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