{"id":679,"date":"2025-03-09T15:00:47","date_gmt":"2025-03-09T15:00:47","guid":{"rendered":"https:\/\/as.vanderbilt.edu\/newmath2025\/?p=679"},"modified":"2025-04-17T15:12:25","modified_gmt":"2025-04-17T15:12:25","slug":"topology-and-group-theory-seminar-april-9-2025","status":"publish","type":"post","link":"https:\/\/as.vanderbilt.edu\/math\/2025\/03\/09\/topology-and-group-theory-seminar-april-9-2025\/","title":{"rendered":"Topology and Group Theory Seminar: April 9, 2025"},"content":{"rendered":"<p><strong>Speaker<\/strong>: John Ratcliffe (Vanderbilt)<\/p>\n<p><strong>Title:<\/strong><strong>\u00a0<\/strong>\u00a0<em>The G-index of a spin closed hyperbolic 4-manifold M<\/em><\/p>\n<p><strong>Abstract:<\/strong><strong>\u00a0<\/strong>In this talk, we will show how to compute the\u00a0<em>G<\/em>-index of a spin closed hyperbolic 4-manifold\u00a0<em>M<\/em>\u00a0for a group\u00a0<em>G<\/em>\u00a0of symmetries of a spin structure on\u00a0<em>M<\/em>. As an example, we will compute the\u00a0<em>G<\/em>-index for the group\u00a0<em>G<\/em>\u00a0of symmetries of the fully symmetric spin structure on the Davis closed hyperbolic 4-manifold\u00a0<em>M<\/em>. Our talk will involve finite groups, infinite discrete groups, and Lie groups. The talk is based on joint work with Steven Tschantz.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Speaker: John Ratcliffe (Vanderbilt) Title:\u00a0\u00a0The G-index of a spin closed hyperbolic 4-manifold M Abstract:\u00a0In this talk, we will show how to compute the\u00a0G-index of a spin closed hyperbolic 4-manifold\u00a0M\u00a0for a group\u00a0G\u00a0of symmetries of a spin structure on\u00a0M. As an example, we will compute the\u00a0G-index for the group\u00a0G\u00a0of symmetries of the fully symmetric spin structure on&#8230;<\/p>\n","protected":false},"author":74,"featured_media":736,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[12,6],"tags":[],"acf":[],"jetpack_featured_media_url":"https:\/\/as.vanderbilt.edu\/math\/wp-content\/uploads\/sites\/69\/2025\/03\/topology-grouptheory.png","_links":{"self":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/679"}],"collection":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/users\/74"}],"replies":[{"embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/comments?post=679"}],"version-history":[{"count":1,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/679\/revisions"}],"predecessor-version":[{"id":680,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/679\/revisions\/680"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/media\/736"}],"wp:attachment":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/media?parent=679"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/categories?post=679"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/tags?post=679"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}