Math 866

MWF 9:30 - 10:18 in Smith Lab 2186

Texts:

1.  John Milnor, Topology from the Differentiable Viewpoint, Princeton University Press, Princeton (1965).  djvu
        ISBN13: 978-0-691-04833-8

2. I.M. Singer and J.A. Thorpe, Lecture Notes on Elementary Topology and Geometry, (Undergraduate Texts in Math.), Springer (1967). pdf
        ISBN 0-387-90202-3
        ISBN 3-540-90202-3


Other books: Hirsch pdf,  Guillemin-Pollack djvu, Tu pdf, Milnor, Lectures on Differential Topology  pdf,  Milnor, Morse Theory  pdf,  Nicolescu, Morse Theory pdf




Speaking schedule for Milnor's book
Speaker Chapter
 topics
 approx.
dates




Raeyong Kim
 1
 Fund. Thm. of Algebra
 11/13
Jose Cervantes
 2
 Sard's Thm.
 11/16
Robert Hines
 3
 Proof of Sard's Thm.
 11/18
Xiaolei Zhao
 4
 Degree mod 2
 11/20 - 11/23
Kun Wang
 5
 Oriented mflds
 11/23 - 11/25
Ismail Saglam
 6
 Poincare-Hopf Thm.
 11/25
Tao Yang
 7
 Framed cobordism
 11/29



Speaking Schedule for Singer-Thorpe

Speaker
 page
numbers
 old page
numbers
 topic
 approx.
dates





Robert Hines
 118-121
 104-108
 differential forms, exterior algebra
 9/30
Matt Sequin
 121-127
 108-113
 Thm 1 & vector analysis
 10/2
Jenny George
 127-132
 113-117
 Thms 2, 3 & induced map
 10/5 - 10/9
Xiaolei Zhao
 132-135
 117-120
 Inverse Function Thm
 10/9 - 10/12
Tao Yang
 135-140
 120-125
 Implicit Function Thm
 10/12 -10/14
Dong Du
 140-143
 125-127
 vector fields, integral curves
 10/14 - 10/16
Yang Liu
 143-148
 128-132
 orientations
 10/16 - 10/19
Raeyong Kim
 148-152
 132-136
 paracompactness and partitions of unity
 10/21
Jose Cervantes
 78-88
 69-79
 simplicial complexes
 10/23 - 10/26
Tapopriya Majumdar
 153-158
 137-141
 simplicial homology
 10/26 - 10/28
Zhenan Sui
 158-161
 142-145
 Euler characteristic, cohomology
 10/28 - 10/30
Kun Wang
 161-164
 145-147
 Stokes Thm and defn of isomorphism
 10/30  - 11/2
Marc Carnovale
 165-172
 148-154
 Lemmas 1 & 3
 11/4
Ismail Saglam
 172-174
 154-156
 Lemma 2 & completion of proof
 11/9