Math 151c: Algebraic and Differential Topology

Lectures: 10:00--10:55 a.m. on Monday, Wednesday, Friday at 153 Sloan
Instructor: Amin Gholampour
Email address: agholamp@caltech.edu
Office: Sloan 258
Office Hour: 11-12 a.m. on Friday
TA:  Yi-Chih Chiu,      
TA's Office hour: Thursday 4pm at Sloan 356.
Course description:
This is the third course in the year-long graduate sequence in topology. The topics covered are Vector bundles, Characteristic classes, and K-theory.
References:
  • Milnor-Stasheff, Characteristic classes
  • Bott-Tu, Differential forms in Algebraic topology
  • Hatcher, Vector bundles and K-theory
    • Course Policy:
    Grades will be based on weekly assigned homework, and a take-home final. Instead of final it is possible to give a seminar on a topic near the end of classes. The topic for seminar can be fixed within the first two weeks of classes. See below for the list of seminars.
    Homework: Each assignment will be posted here on Friday and it will be due next Friday at 4pm. Discussing assignment is encouraged, but the solutions must be written independently.
    Unless otherwise stated all the assigned problems are from Milnor.
    Assigned problems may also be discussed with the TA (See above for his office hours). 
    1st week PDF                                      Due: 4/10
    2nd week PDF                                      Due: 4/17
    3rd week PDF                                      Due: 4/24
    4th week PDF                                      Due: 5/1
    5th week No Homework for this week! But look at exercises in Chapter 13 for your own benefit.
    6th week PDF                                      Due:5/15
    7th week PDF                                      Due:5/29

    Final

    		 PDF                                      Due:6/3      4pm

    Seminars:

    Speaker(s)

    Title

    Date/place

    Bartlett

    		 Manifolds homeomorphic to the 7-sphere May 26, 3-3:50pm  at  Sloan 153
    Wong Schubert calculus I May 26, 4-4:50pm  at  Sloan 153
    Garrel-Chung Schubert calculus II-Lines on algebraic varieties May 27, 3-4:50pm  at  Sloan 153
    Goto Morse homology May 28, 3-3:50pm  at  Sloan 153
    Frankel Affine foliations and affine manifolds May 28, 4-4:50pm  at  Sloan 153
    Teh-Venkateswaran Existence of Steifel-Whitney classes May 27 and 29 during class time.