lectures on dierential geometry math 240bc john douglas moore department of mathematics university of california santa barbara ca usa 93106 e mail moore math ucsb edu june 5 2009 preface ...
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...Lectures on dierential geometry math bc john douglas moore department of mathematics university california santa barbara ca usa e mail ucsb edu june preface this is a set lecture notes for the course given during winter and spring evolved as progressed are still somewhat rough but we hope they helpful starred sections represent digressions less central to core subject matter can be omitted rst reading our goal was present key ideas riemannian up generalized gauss bonnet theorem chapter provides foundational results second an introduction de rham cohomology which prehaps simplest notion homology that so pervasive in modern andtopology third provide some basic relating curvature topology manifold idea here develop intuition finally fourth describe cartan s method moving frames focus its application one theorems last more advanced nature not usually treated year it theory characteristic classes explaining how these could generated by looking extensions describes applications atiyah singer...