The problem of determining when a smooth compact manifold admits a positive-scalar-curvature (psc) Riemannian metric is comparatively well understood. However, even for the n-sphere, surprisingly little work has been done to date concerning the topological stucture of the moduli space of all psc metrics modulo diffeomorphisms. In this talk, I will present some new results concerning the rational homotopy groups of this space for the n-sphere with n>4. My approach uses results on higher analytical/topological torsion due to Hatcher, Igusa, and Goethe. |
Department of Mathematics, University of Oregon, Eugene OR 97403
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