{"id":173,"date":"2005-03-27T16:19:47","date_gmt":"2005-03-27T20:19:47","guid":{"rendered":"http:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=173"},"modified":"2005-03-27T16:19:47","modified_gmt":"2005-03-27T20:19:47","slug":"new-this-weeks-finds","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=173","title":{"rendered":"New This Week&#8217;s Finds"},"content":{"rendered":"<p>John Baez has just put out a <A href=\"http:\/\/math.ucr.edu\/home\/baez\/week212.html\">new issue<\/A> of his <A href=\"http:\/\/math.ucr.edu\/home\/baez\/TWF.html\">This Week&#8217;s Finds in Mathematical Physics<\/A>, dealing partly in more detail with the material about Clifford modules mentioned <A href=\"http:\/\/www.math.columbia.edu\/~woit\/blog\/archives\/000166.html\">here<\/A> a couple weeks ago.  I&#8217;ve added as the first comment here something he had some trouble submitting as a comment to the older posting on this topic.<\/p>\n<p>John briefly mentions a relation of all this to Bott periodicity in topology, using a very abstract homotopy construction involving spectra.  A more concrete version of this can be found in Milnor&#8217;s book on Morse theory.  For the relation of Clifford algebras and K-theory, the standard refererence is the 1964 paper &#8220;Clifford Modules&#8221; by Atiyah, Bott and Shapiro published in the journal &#8220;Topology&#8221;. The crucial fact they describe is how the Thom isomorphism in K-theory (which is essentially the same fact as Bott periodicity) is related to the structure of Clifford modules. Greg Landweber has recently worked out an interesting <A href=\"http:\/\/www.arxiv.org\/abs\/math.RT\/0403203\">equivariant version<\/A> of this story.   <\/p>\n<p>Greg also has a nice <A href=\"http:\/\/math.uoregon.edu\/%7Egreg\/KthySurj.pdf\">new paper<\/A> with Megumi Harada about the K-theory of a symplectic quotient, that looks like it should imminently appear on the arXiv.<\/p>\n<p>John also mentions some recent work of Dror Bar-Natan, Thang Le and Dylan Thurston on the Duflo isomorphism.  This is a beautiful story, and also has a relation to Clifford algebras that John doesn&#8217;t mention.  For this, see Eckhard Meinrenken&#8217;s <A href=\"http:\/\/www.arxiv.org\/abs\/math.RT\/0304328\">talk<\/A> at the 2002 ICM in Beijing.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>John Baez has just put out a new issue of his This Week&#8217;s Finds in Mathematical Physics, dealing partly in more detail with the material about Clifford modules mentioned here a couple weeks ago. I&#8217;ve added as the first comment &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=173\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[1],"tags":[],"class_list":["post-173","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/173","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=173"}],"version-history":[{"count":0,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/173\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=173"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=173"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=173"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}