tag:blogger.com,1999:blog-56324355175276136382014-10-01T21:37:04.047-07:00Classics SeminarJoseph Coffeyhttp://www.blogger.com/profile/09814174644942173398noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-5632435517527613638.post-31380133497299745022007-04-10T12:46:00.000-07:002007-04-11T11:49:57.461-07:00PapersThe following reading list depends heavily on Ralph Cohen's advice. Much of the material is summarized in Ralph's <a href="http://www.amazon.com/Topology-Homology-Advanced-Courses-Mathematics/dp/3764321822/ref=sr_1_1/104-0672395-0930319?ie=UTF8&s=books&qid=1176316722&sr=8-1">lecture notes</a> written with Voronov. In particular those notes have (I hear) a good bibliography.<br /><br />We will begin with Sullivan and Chas's, definition of the S<a href="http://front.math.ucdavis.edu/math.GT/9911159">tring operations on the loop space</a>: <br /><br />Definitions of cyclic/hoschshild homology: For cyclic we have Connes' original paper, or the Loday-Quillen<br />paper, which gives a modern approach. <br /><br />General relation of Hochshild and cyclic homology to the homology of loop<br />spaces: J. Jones' paper, "Cyclic homology and equivariant homology, Inventionnes, 87 (1987), 403-423.<br /><br />Minimal models: D. Sullivan, "Infinitesimal computations in topology" Publ. IHES , 47 (1977) pp. 269–331 <br /><br />How the hochshild cohomology under cup product, coincides with the Chas-Sullivan product under the Jones<br />isomorphism: Ralph's paper with Jones, "A homotopy theoretic realization of string topology", Math. Ann. 324 (2002), 773-798.<br /><br />Another approach which is simpler (although only works over the reals) using differential forms and Sullivan minimal models is due to <a href="http://front.math.ucdavis.edu/math.AT/0309038">S.A. Merkulov "A deRham model for string topology"</a>Joseph Coffeyhttp://www.blogger.com/profile/09814174644942173398noreply@blogger.com0tag:blogger.com,1999:blog-5632435517527613638.post-62877975945225498612007-04-09T15:27:00.000-07:002007-04-09T15:32:04.148-07:00ThemeThe theme, at least for the first half of the quarter, will be the homological algebra and geometry of the loop space.<br /><br />i) The String product (Sullivan and Chas)<br />ii) Definitions of Hoschild and cyclic cohomology of an algebra<br />iii) Relationship of the string product to Hoschild and cyclic cohomology on chains of loops space<br />iv) Relationship of the string product to the Symplectic Field Theory of the cotangent bundleJoseph Coffeyhttp://www.blogger.com/profile/09814174644942173398noreply@blogger.com0