Session S23 - Group actions in Differential Geometry

Friday, July 16, 19:40 ~ 20:10 UTC-3

$SO(2)\times SO(3)$-invariant Ricci solitons and ancient flows on $\mathbb{S}^4$

Timothy Buttsworth

The University of Queensland, Australia   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

A full understanding of the behaviour of a Ricci flow near a singularity typically requires a classification of the possible Ricci solitons that can occur as singularity models. Such a classification exists for three-dimensional manifolds, but remains elusive for higher-dimensional manifolds. In this talk, I will describe recent attempts to understand the possible gradient shrinking Ricci solitons which can occur on $\mathbb{S}^4$ that are invariant under the usual group action of $SO(2)\times SO(3)$. It appears that the only such solitons are round, but our analysis also reveals the existence of a somewhat novel $\kappa$-noncollapsed ancient Ricci flow on $\mathbb{S}^4$.

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