Viktor Majewski, University of Waterloo
Filling Holes in the Spin(7)-Teichmüller Space and String Cohomology
In this talk, I apply the analytic results from the first talk to study the boundary of the Spin(7) Teichmüller space. Using compactness results for Ricci-flat metrics together with known examples of Spin(7) manifolds, it is known that Spin(7) orbifolds with SU(N) isotropy arise as boundary points of the moduli space.
Building on the resolution scheme for Spin(7) orbifolds that I discussed in 2024, and which I will briefly review, we show how this boundary can be removed by requiring Spin(7) orbifolds to encode information about their resolutions. In this way, the Teichmüller space is enlarged to include orbifold limits together with their compatible resolutions, thereby filling in the boundary.
Finally, we explain how this perspective is related to a Spin(7) analogue of the crepant resolution conjecture from string cohomology, providing a geometric interpretation of the obstruction complex discussed in the linear gluing analysis in the first talk.
MC 5403