## View abstract

### 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. document.getElementById('cloak6751f9699b46c438acec5554d34259f8').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy6751f9699b46c438acec5554d34259f8 = 't.b&#117;ttsw&#111;rth' + '&#64;'; addy6751f9699b46c438acec5554d34259f8 = addy6751f9699b46c438acec5554d34259f8 + '&#117;q' + '&#46;' + '&#101;d&#117;' + '&#46;' + '&#97;&#117;'; var addy_text6751f9699b46c438acec5554d34259f8 = 't.b&#117;ttsw&#111;rth' + '&#64;' + '&#117;q' + '&#46;' + '&#101;d&#117;' + '&#46;' + '&#97;&#117;';document.getElementById('cloak6751f9699b46c438acec5554d34259f8').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy6751f9699b46c438acec5554d34259f8 + '\'>'+addy_text6751f9699b46c438acec5554d34259f8+'<\/a>';

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 $\mathbb{S}^4$.