[{"key":"dc.contributor.author","value":"Yagi, Toshiyuki","language":null},{"key":"dc.date.accessioned","value":"2010-01-22T23:33:01Z","language":null},{"key":"dc.date.available","value":"2010-01-22T23:33:01Z","language":null},{"key":"dc.date.issued","value":"1973","language":null},{"key":"dc.identifier.uri","value":"http:\/\/hdl.handle.net\/2429\/19060","language":null},{"key":"dc.description.abstract","value":"For any two differential modules M and N over a graded differential k-algebra \u039b\r\n(k a commutative ring), there Is a spectral sequence Er, called the Eilenberg-Moore spectral sequence, having the following properties: Er converges to Tor \u039b (M,N) and E2=TorH(\u039b) (H(M),H(N)). This algebraic set-up gives rise to a \"geometric\" spectral sequence in algebraic topology. Starting with a commutative diagram of topological spaces [diagram omitted]\r\nwhere B Is simply connected, one gets a spectral sequence Er converging to the cohomology H*(X xBY) of the space X xBY,\r\nand for which E\u2082=TorH*(B) (H*(X),H*(Y)).\r\nIn this thesis we outline a generalization of the above geometric spectral sequence obtained, by first extending the\r\ncategory of topological spaces and then, extending the cohomology theory H* to this larger category. The convergence of the extended spectral sequence does not depend, on any topological\r\nconditions of the spaces involved. It follows algebraically\r\nfrom the way the exact couple (from which the spectral sequence Is derived) Is set up and from the Suspension\r\nAxiom of the extended cohomology theory.","language":"en"},{"key":"dc.language.iso","value":"eng","language":"en"},{"key":"dc.publisher","value":"University of British Columbia","language":null},{"key":"dc.rights","value":"For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https:\/\/open.library.ubc.ca\/terms_of_use.","language":null},{"key":"dc.subject","value":"Eilenberg-Moore spectral sequences","language":"en"},{"key":"dc.title","value":"The Eilenberg-Moore spectral sequence","language":"en"},{"key":"dc.type","value":"Text","language":null},{"key":"dc.degree.name","value":"Master of Science - MSc","language":"en"},{"key":"dc.degree.discipline","value":"Mathematics","language":"en"},{"key":"dc.degree.grantor","value":"University of British Columbia","language":null},{"key":"dc.type.text","value":"Thesis\/Dissertation","language":"en"},{"key":"dc.description.affiliation","value":"Science, Faculty of","language":null},{"key":"dc.description.affiliation","value":"Mathematics, Department of","language":null},{"key":"dc.degree.campus","value":"UBCV","language":"en"},{"key":"dc.description.scholarlevel","value":"Graduate","language":"en"}]