Department of Mathematics: Graduate Seminar Series

Title: Cohomogeneity One Expanding Ricci Solitons and the Expander Degree

Abstract: We consider the space of smooth gradient expanding Ricci soliton structures on S1×R3 and S2×R2 which are invariant under the action of SO(3)×SO(2). In the case of each topology, there exists a 2-parameter family of cohomogeneity one solitons asymptotic to cones over the link S2×S1, as constructed by Nienhaus-Wink and Buzano-Dancer-Gallaugher-Wang. Analogous to work of Bamler and Chen, we define a notion of expander degree for these cohomogeneity one solitons through a properness result. We then proceed to calculate this cohomogeneity one expander degree in the cases of the specific topologies.