tag:blogger.com,1999:blog-25263521392140118342015-09-16T17:29:33.087-07:00Math 217A Differential GeometryA first course in Differential Geometry, covering: Vector bundles -including the tangent bundle, vector fields, differential forms, Riemannian metrics, symplectic structures, and a general discussion of tensors, and connections from a variety of viewpoints. Depending on time and the sophistication of the audience we will proceed to more advanced subjects. For example a discussion of the h-principle and its role in differential geometry.Joseph Coffeyhttp://www.blogger.com/profile/09814174644942173398noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-2526352139214011834.post-15673851028129326292006-10-17T10:07:00.001-07:002006-10-18T07:51:16.262-07:00HW 2 Due Next MondayChapter 5, #17<br />Chapter 6, #7<br />Chapter 7, # 6<br />Chapter 7, #11<br />Show that the distribution in R3 given by the equation:<br /> d z - y d x = 0<br />is nowhere integrable.Joseph Coffeyhttp://www.blogger.com/profile/09814174644942173398noreply@blogger.com0tag:blogger.com,1999:blog-2526352139214011834.post-17565849274996114622006-10-04T12:10:00.000-07:002006-10-04T12:11:12.276-07:00HW 1Here is the homework assignment. It is due next Wed.<br /><br />Chapt 2 (Vol 1) of Spivak 3,11<br /><br />Show that if M is a smooth n manifold, and N is a smooth k-manifold, and f:M->N is a surjective, smooth map then there a set of full measure U in N, such that for each x in U, f^-1(x) is a smooth n-k manifold.<br /><br />Show that a bundle E is orientable if and only if /\^n(E) admits a no where vanishing section. (The crazy asci mess there denote the highest wedge power of E). Show that E is orientable if and only if its dual is.<br /><br />Chapter 3, number 27<br /><br />Chapter 4 numbers 1,8Joseph Coffeyhttp://www.blogger.com/profile/09814174644942173398noreply@blogger.com0tag:blogger.com,1999:blog-2526352139214011834.post-15151701156431631152006-09-22T10:08:00.000-07:002006-09-22T10:15:10.461-07:00Syllabus, course text etc...The basic "reference" text for the course will be Spivak, volume 1 and 2. The first portion of this course is a discussion of the language of modern differential geometry. Since the first year sequence now includes some of this language we will proceed quite quickly through the initial definitions. Spivak proceeds quite leisurely, so do not be alarmed at the apparently breakneck pace through the book.Joseph Coffeyhttp://www.blogger.com/profile/09814174644942173398noreply@blogger.com0