Math 6510 - 1 Additional Texts

Course Title: Differentiable Manifolds
Course Number: MATH 6510 - 1
Instructor: Andrejs Treibergs
Home Page: http://www.math.utah.edu/~treiberg/M6510.html
Place & Time: M, W, F, 10:45 - 11:35 in LCB 333
Office Hours: 11:45-12:45 M, W, F, in JTB 120 (tent.)
E-mail: treiberg@math.utah.edu
Prerequisites: Prerequisites: "C" or better in MATH 4510 AND MATH 5520 or consent of instructor.
Main Text: Math 6510 Notes by Kevin Wortman
http://www.math.utah.edu/~wortman/6510.pdf


We shall basically follow the text. But much of the material is standard and widely available. I'll provide references and put copies in the math library. I will also cover additional topics that were suggested in consultation with Professors Bestvina, Bromberg and Wortman. Come to class for details and references. Here is a partial list of alternative sources that cover the material.

I have tried several different texts for this course: Bredon, Guillemin and Pollack, Singer and Thorpe, Spivak, Sternberg and Warner. Perhaps not so unexpectedly, the texts the students liked the best, Guillemin & Pollack and Singer & Thorpe are not the ones I liked the best, Bredon, Sternberg and Warner. None of the texts perfectly suits the material we teach at the University of Utah.

This course is designed to be a balance of application and theory that is optimized for the needs of students at Utah, be they interested in algebraic geometry, commutative algebra, geometric group theory, representation theory or geometric analysis. As mathematicians, it is our prerogative and, indeed duty, to understand why theorems work, so that we may modify or code them as we encounter them in the future.

The choice of topics in Math 6510 varies slightly from instructor to instructor, although the variance is far less than you might think hearing old graduate student gossip. One only needs to look at previous syllabi, or the Geometry / Topology Preliminary Exams derived from these courses over the last decade to see that they are very consistent. Guillemin & Pollack's text spins toward transversality theory. Wortman's notes designed for this course spin toward Lie Groups. A course based on John Lee's text spins towards differential geometry.

Texts Written for an Undergraduate Course in Differentiable Manifolds.

Texts Suitable for a Graduate Course in Differentiable Manifolds.

Specialist's Books on Specific Topics. Unsuitable for Math 6510.