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SUMMARY:Torsion obstructions to positive scalar curvature - Bernhard  Hank
 e (Universität Augsburg)
DTSTART:20240621T101500Z
DTEND:20240621T111500Z
UID:TALK217411@talks.cam.ac.uk
DESCRIPTION:In 1998\, Thomas Schick discovered a homological obstruction t
 o the existence of positive scalar curvature metrics on oriented closed sm
 ooth manifolds in terms of torality properties of their fundamental classe
 s. We will combine this obstruction with the enlargeability obstruction to
  positive scalar curvature metrics introduced by Gromov and Lawson in the 
 1980s. Surprisingly\, the resulting invariant is of a purely group homolog
 ical nature.\nAs an application we construct new examples of manifolds whi
 ch do not admit positive scalar curvature metrics\, but whose Cartesian pr
 oducts admit such metrics.&nbsp\;\nSeveral basic questions remain open. Th
 e most important is whether toral manifolds of dimension at least 4 with f
 inite fundamental groups of odd order admit positive scalar curvature metr
 ics.&nbsp\;\nThis talk is based on joint work with Misha Gromov.\n&nbsp\;\
 n&nbsp\;\n&nbsp\;\n&nbsp\;
LOCATION:External
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