{"id":483,"date":"2016-04-13T19:34:42","date_gmt":"2016-04-13T16:34:42","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=483"},"modified":"2016-04-21T11:33:49","modified_gmt":"2016-04-21T08:33:49","slug":"colloquium-tuesday-april-19-2-pm-speaker-emmanuel-farjoun-hebrew-university-title-a-homotopy-path-from-groups-to-topological-groups","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=483","title":{"rendered":"Colloquium: Tuesday, April 19, 2 pm. Speaker: Emmanuel Farjoun (Hebrew University). Title: &#8220;A homotopy path from groups to topological groups&#8221;."},"content":{"rendered":"<div dir=\"ltr\">\n<div class=\"gmail_default\">Given a map of discrete groups f:G &#8211;&gt; H when is this map induced from a normal subgroup inclusion of topological groups X \\subseteq Y by taking path components of X and Y?For example, the trivial map on the integers \\mathbb{Z} \\to 0 arises in this way via the inclusion \\mathbb{Z} \\subseteq \\mathbb{R} of the integers in the additive group of real numbers. However the trivial map on a non commutative group G \\to 1 cannot arise from such a normal inclusion of topological groups.<\/p>\n<p>In considering this question one builds from the given map f of discrete groups an associated topological space Q:= H\/\/G, the homotopy quotient, and attempts to put a group structure on Q. This is not possible in general, in particular if Q has non abelian fundamental group.<\/p>\n<p>We will discuss similar constructions and show that the answer to the above question lies with a well known notion of crossed module and an observation due to Quillen.<\/p>\n<p>This is joint work with Segev.<\/p>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Given a map of discrete groups f:G &#8211;&gt; H when is this map induced from a normal subgroup inclusion of topological groups X \\subseteq Y by taking path components of X and Y?For example, the trivial map on the integers&#8230;<br \/><a class=\"read-more-button\" href=\"https:\/\/mathematics.haifa.ac.il\/?p=483\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-483","post","type-post","status-publish","format-standard","hentry","category-colloquium"],"_links":{"self":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/483","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=483"}],"version-history":[{"count":2,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/483\/revisions"}],"predecessor-version":[{"id":485,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/483\/revisions\/485"}],"wp:attachment":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=483"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=483"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=483"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}