RUI: Quotient Spaces and the Double Soul Conjecture

The Principal Investigator will investigate shapes called manifolds which are of particular importance due to the critical role they play in Einstein's general theory of relativity. His main focus will be on a special class of manifolds which are called double disk bundles. The PI intends to increase our understanding of the relationships which exist between double disk bundles and other important classes of manifolds. The PI will accomplish this via projects ranging in scope from undergraduate research experiences to international collaborations. The PI's work, motivated by the Double Soul Conjecture and the recent introduction of codimension one biquotient foliations, seeks to improve our understanding of double disk bundles both topologically and geometrically. From the topological side, he intends to increase our understanding of when certain spaces of geometric interest, such as homogeneous spaces and biquotients, carry a double disk bundle structure. On the geometric side, he intends to use double disk bundle structures in the construction of new examples of manifolds with interesting Riemannian metrics. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.