{"id":1584,"date":"2026-02-28T20:37:58","date_gmt":"2026-03-01T04:37:58","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/hades\/?p=1584"},"modified":"2026-03-09T15:38:39","modified_gmt":"2026-03-09T22:38:39","slug":"cohomogeneity-one-expanding-ricci-solitons-and-the-expander-degree","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2026\/02\/28\/cohomogeneity-one-expanding-ricci-solitons-and-the-expander-degree\/","title":{"rendered":"Cohomogeneity One Expanding Ricci Solitons and the Expander Degree"},"content":{"rendered":"<p>The HADES seminar on Tuesday, <strong>March <\/strong><b>3rd<\/b>, will be at\u00a0<strong>3:30pm<\/strong>\u00a0in\u00a0<strong>Room 740<\/strong>.<\/p>\n<p><strong>Speaker:\u00a0<\/strong>Abishek Rajan<\/p>\n<p><strong>Abstract:\u00a0<\/strong>We consider the space of smooth gradient expanding Ricci soliton structures on <img loading=\"lazy\" decoding=\"async\" id=\"l0.10154633957625514\" class=\"va_li\" title=\"S^1\\times \\mathbb R^3\" src=\"https:\/\/s0.wp.com\/latex.php?zoom=3&amp;bg=ffffff&amp;fg=000000&amp;s=0&amp;latex=S%5E1%5Ctimes%09%5Cmathbb%09R%5E3\" alt=\"S^1\\times \\mathbb R^3\" width=\"54\" height=\"13\" \/> and <img loading=\"lazy\" decoding=\"async\" id=\"l0.4308622797188567\" class=\"va_li\" title=\"S^2\\times \\mathbb R^2\" src=\"https:\/\/s0.wp.com\/latex.php?zoom=3&amp;bg=ffffff&amp;fg=000000&amp;s=0&amp;latex=S%5E2%5Ctimes%09%5Cmathbb%09R%5E2\" alt=\"S^2\\times \\mathbb R^2\" width=\"54\" height=\"13\" \/> which are invariant under the action of <img loading=\"lazy\" decoding=\"async\" id=\"l0.22417445226227628\" class=\"va_li\" title=\"SO(3)\\times SO(2)\" src=\"https:\/\/s0.wp.com\/latex.php?zoom=3&amp;bg=ffffff&amp;fg=000000&amp;s=0&amp;latex=SO(3)%5Ctimes%09SO(2)\" alt=\"SO(3)\\times SO(2)\" width=\"107\" height=\"16\" \/>. In the case of each topology, there exists a 2-parameter family of cohomogeneity one solitons asymptotic to cones over the link <img loading=\"lazy\" decoding=\"async\" id=\"l0.30207191340847594\" class=\"va_li\" title=\"S^2\\times S^1\" src=\"https:\/\/s0.wp.com\/latex.php?zoom=3&amp;bg=ffffff&amp;fg=000000&amp;s=0&amp;latex=S%5E2%5Ctimes%09S%5E1\" alt=\"S^2\\times S^1\" width=\"52\" height=\"13\" \/>, 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<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday, March 3rd, will be at\u00a03:30pm\u00a0in\u00a0Room 740. Speaker:\u00a0Abishek Rajan Abstract:\u00a0We consider the space of smooth gradient expanding Ricci soliton structures on and which are invariant under the action of . In the case of each topology, there exists a 2-parameter family of cohomogeneity one solitons asymptotic to cones over the link [&hellip;]<\/p>\n","protected":false},"author":95,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[26,1],"tags":[],"class_list":["post-1584","post","type-post","status-publish","format-standard","hentry","category-spring-2026","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1584","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/users\/95"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=1584"}],"version-history":[{"count":1,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1584\/revisions"}],"predecessor-version":[{"id":1585,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1584\/revisions\/1585"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=1584"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=1584"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=1584"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}