Fall 2015 Course Syllabus - Mathematics 9071.001
Course: Mathematics 9071.001.
Course Title: Topics in Differential Topology.
Time: 9:30-10:50.
Place: Wachman 527.
Instructor: Mendoza, Gerardo A.
Instructor Office: Wachman 618.
Instructor Email: gerardo.mendoza@temple.edu
Instructor Phone: 1-5053.
Course Web Page: http://math.temple.edu/~gmendoza/
Office Hours: by appointment.
Prerequisites: Basic knowledge about differentiable manifolds and algebraic topology.
Textbook: No textbook; notes will be distributed as the semester progresses.
References:
Husemoller, Fibre bundles. GTM 20. Springer-Verlag, New York, 1994.
Kobayashi, Differential geometry of complex vector bundles, Princeton University Press, 1987.
Course Goals: To acquire a deep understanding of various aspects of vector bundles, in particular in connection with partial differential equations.
Topics Covered: This is a one semester course on differential-topological aspects of vector bundles, including interconnections with global properties of partial differential equations. Topics include a prelude on general fiber bundles, after which the course turns specific to vector bundles: characteristic classes, connections and curvature, flat and holomorphic vector bundles; in the latter context also vanishing theorems. Finally, various ways in which vector bundles arise, or lead to, or are relevant in partial differential equations, for instance differential complexes, Dirac operators, and a careful description of the Atiyah-Singer index theorem.
Course Grading: This is an advanced course, there will be no exams. However, active participation is expected and will be rewarded accordingly.
Exam Dates: This is an advanced course, there will be no exams.
Attendance Policy: Attendance is required. Missing four classes implies a failing grade.
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