{"id":640,"date":"2024-10-07T23:21:33","date_gmt":"2024-10-07T23:21:33","guid":{"rendered":"https:\/\/as.vanderbilt.edu\/newmath2025\/?p=640"},"modified":"2025-03-11T18:53:12","modified_gmt":"2025-03-11T18:53:12","slug":"geometry-and-topology-seminar-friday-october-4th","status":"publish","type":"post","link":"https:\/\/as.vanderbilt.edu\/math\/2024\/10\/07\/geometry-and-topology-seminar-friday-october-4th\/","title":{"rendered":"Geometry and Topology Seminar: October 4, 2024"},"content":{"rendered":"<p><strong>Speaker:<\/strong>\u00a0Sofia Martinez Alberga\u00a0(Purdue University)<\/p>\n<p><strong>Title:<\/strong><strong>\u00a0<\/strong>Modeling Equivariant Simplicial Sets with Simplicial Coalgebras<strong><br \/>\n<\/strong><\/p>\n<p><strong>Abstract:<\/strong><strong>\u00a0<\/strong>Given a commutative ring R, a $\\pi_1$-R-equivalence is a continuous map of spaces inducing an isomorphism on\u00a0fundamental groups and an R-homology equivalence between universal covers. When R is an algebraically closed field, Raptis and Rivera described a full and faithful model for the homotopy theory of spaces up to $\\pi_1$-R-equivalence. They did<br \/>\nthis by means of simplicial coalgebras considered up to a notion of weak equivalence created by a localized version of the cobar\u00a0functor. In this article, we prove a G-equivariant analog of this statement using generalizations of a celebrated theorem of Elmendorf. We also prove a more general result about modeling $G$-simplicial sets considered under a linearized version of quasi-categorical\u00a0equivalence in terms of simplicial coalgebras.<\/p>\n<p><strong>Contact<\/strong>: <a href=\"mailto:hannah.housden@vanderbilt.edu\">Hannah Housden<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Speaker:\u00a0Sofia Martinez Alberga\u00a0(Purdue University) Title:\u00a0Modeling Equivariant Simplicial Sets with Simplicial Coalgebras Abstract:\u00a0Given a commutative ring R, a $\\pi_1$-R-equivalence is a continuous map of spaces inducing an isomorphism on\u00a0fundamental groups and an R-homology equivalence between universal covers. When R is an algebraically closed field, Raptis and Rivera described a full and faithful model for the homotopy&#8230;<\/p>\n","protected":false},"author":74,"featured_media":751,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[9],"tags":[],"acf":[],"jetpack_featured_media_url":"https:\/\/as.vanderbilt.edu\/math\/wp-content\/uploads\/sites\/69\/2025\/03\/geometry-topology.png","_links":{"self":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/640"}],"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=640"}],"version-history":[{"count":2,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/640\/revisions"}],"predecessor-version":[{"id":659,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/640\/revisions\/659"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/media\/751"}],"wp:attachment":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/media?parent=640"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/categories?post=640"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/tags?post=640"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}