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SUMMARY:Gyration Stability for Projective Planes - Sebastian Chenery (Univ
 ersity of Southampton)
DTSTART:20240621T124500Z
DTEND:20240621T131500Z
UID:TALK217414@talks.cam.ac.uk
DESCRIPTION:Gyrations are operations on manifolds that arise in geometric 
 topology\, where a manifold M may exhibit multiple gyrations depending on 
 the chosen "twisting." A natural question arises: for a given M\, do all g
 yrations share the same diffeomorphism\, homeomorphism\, or homotopy type 
 regardless of the twisting? This property is known as gyration stability. 
 Inspired by recent work by Duan\, which demonstrated that the quaternionic
  projective plane is not gyration stable (with respect to diffeomorphism) 
 by invoking spin structures\, we will explore gyration stability of projec
 tive planes from the homotopy theoretic perspective. Our generalization pr
 ovides new results and leads to a complete description of gyration stabili
 ty for the complex\, quaternionic\, and octonionic projective planes. This
  is joint work with Stephen Theriault.
LOCATION:External
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