Abstract:
Gromov defined macroscopic dimension of metric spaces to study manifolds admitting a Positive Scaler Curvature (PSC) metric, via their largeness properties. He conjectured universal cover of PSC n-manifolds should have macroscopic dimension at most n-2. This conjecture depends heavily on the fundamental group of the n-manifold. Under the assumption of the Strong Novikov Conjecture, we prove that closed spin manifolds having fundamental group a Graph Product of geometrically finite groups satisfies the conjecture, provided the vertex groups have classifying space which becomes wedge sum of Moore Spaces, after finitely many suspension. This generalizes our previous result when the fundamental group is a RAAG. We developed a crucial property called 1-Step Stabilization Property (1-SSP) for groups to prove the above. We also found an examples of groups not satisfying 1-SSP, inspiring more investigation towards possible counter example related to Gromov’s conjecture.
Scheduled for: 2026-03-13 03:40 PM: GeoTop Session #6.1 in Heritage Hall Building 126
Status: Accepted
Collection: Geometric Topology
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