{"id":43,"date":"2016-10-10T10:46:57","date_gmt":"2016-10-10T09:46:57","guid":{"rendered":"http:\/\/blogs.kent.ac.uk\/pgrseminars\/?p=43"},"modified":"2016-10-12T12:49:06","modified_gmt":"2016-10-12T11:49:06","slug":"7-october-2016-christos-sarakisidis-homology-and-cohomology-theories-a-historical-survey-and-the-contemporary-approach","status":"publish","type":"post","link":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/2016\/10\/10\/7-october-2016-christos-sarakisidis-homology-and-cohomology-theories-a-historical-survey-and-the-contemporary-approach\/","title":{"rendered":"7 October 2016: Christos Sarakisidis &#8220;Homology and Cohomology theories: a historical survey and the contemporary approach&#8221;"},"content":{"rendered":"<p><span style=\"font-family: 'Calibri',sans-serif;color: black\">Homology and years after Cohomology became the main object\u00a0of study for many\u00a0 areas of mathematics the last 150 years or so. The reason is that they both provide a very powerful machinery for classifying objects (especially geometrical like topological, differentiable manifolds, CW complexes, Schemes, Varieties\u00a0etc.) but each one from a different point of view. Whilst the above terms are referring usually to the so-called singular\u00a0(co)homology theory these two notions have been expanded through Category Theory as\u00a0a tool in many other areas like Algebraic Geometry, Algebraic Topology, Simplicial Homotopy Theory, Homological Algebra etc. In this talk we will focus\u00a0mainly on\u00a0understanding the basic idea behind those things through some explicit calculations and the uniqueness of such a theory via the Eilenberg-Steenrod axioms.\u00a0<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Homology and years after Cohomology became the main object\u00a0of study for many\u00a0 areas of mathematics the last 150 years or so. The reason is that &hellip; <a href=\"https:\/\/blogs.kent.ac.uk\/pgrseminars\/2016\/10\/10\/7-october-2016-christos-sarakisidis-homology-and-cohomology-theories-a-historical-survey-and-the-contemporary-approach\/\">Read&nbsp;more<\/a><\/p>\n","protected":false},"author":2347,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[170524],"tags":[],"_links":{"self":[{"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/posts\/43"}],"collection":[{"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/users\/2347"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/comments?post=43"}],"version-history":[{"count":1,"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/posts\/43\/revisions"}],"predecessor-version":[{"id":44,"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/posts\/43\/revisions\/44"}],"wp:attachment":[{"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/media?parent=43"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/categories?post=43"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/tags?post=43"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}