Symmetric Approach to General Relativity - Applications to Exotic Spheres

Explore a symmetric approach to General Relativity and its applications to exotic spheres in this 58-minute lecture by Leonardo Cavenaghi from CAMPINAS at the University of Miami. Delve into the Cheeger deformation procedure, initially developed in the 1970s by Jeff Cheeger, and its use in producing manifolds with non-negative sectional curvature. Examine how this technique can be applied to various dimensional spaces, including R^4, S^3, and S^7 or Sigma^7 (exotic spheres). Investigate the implications of using exotic spheres in physical models, particularly focusing on the lack of isotropy in Riemannian metrics on Sigma^7. Discover how S^1-actions on these manifolds lead to fixed points and the creation of global Lorentzian metrics with similar geometric properties, suggesting that smooth structures may not significantly impact physics in compact models. Gain insights into this collaborative research with Prof. Lino Grama, bridging advanced mathematics and theoretical physics.