Math 534A Geometry-Topology: Fall 2020
Instructor:
Doug Pickrell
Office: Math 703
Official Office Hours: each day after
class (but my office door is open
most of the day, and I welcome reasonable questions)
Email: pickrell@math.arizona.edu
Phone: 621-4767
Recommended Text:
Michael Spivak
A Comprehensive Introduction to Differential Geometry, Vol 1, any edition.
This is a leisurely written book,
perhaps a bit too wordy for some tastes. In the Fall semester we will cover chapters 1, 2, 3, 4, 5,
7, and 8. At the end of the Spring semester, we will
return to cover chapter 11.
Here are two books which cover essentially the same material
as in Vol I of Differential Geometry, and which are available online through
the UA library: Introduction to Manifolds by Loring Tu, and
Introduction to Smooth Manifolds by John Lee. A book which nicely
complements Spivak is Differential Topology by Victor Guillemin and Alan
Pollack. Two books which cover some of the same material, but at a lower
level, are Calculus on Manifolds, by Spivak, and Analysis on Manifolds,
by James Munkres.
I will assign homework each Thursday, and each assignment will be due one week later. The final semester grade will be based on homework (40%), one inclass midterm (20%), and the final exam (40%). ``A'' will mean that I believe you are on pace in preparing for the geom-top qualifying exam, ``B'' will mean that you are making significant progress, but are off pace in preparing for the exam.
TA: Either a GTA (or I) will meet with you (on an optional basis) once a week to work on problem assignments (TBA).