RUI: quotient spaces and the double soul conjecture

This National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) project grant provides $136,007 to the University of Tennessee at Martin (UT Martin) from July 1, 2024 to June 30, 2027. The grant supports research on the geometric properties of manifolds, with a focus on understanding the relationships between double disk bundles and other important classes of manifolds. The principal investigator will conduct projects ranging from undergraduate research experiences to international collaborations, aiming to improve the topological and geometric understanding of double disk bundles. This work, motivated by the double soul conjecture and the introduction of codimension one biquotient foliations, seeks to contribute to the broader knowledge of manifolds and their role in Einstein's general theory of relativity. No sub-awards are planned under this grant.

Abstract

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.- subawards are not planned for this award.