Geometry of surfaces (and introduction to three-manifolds)

Jan-April 2016

Vijay Ravikumar (vijayr at cmi dot ac dot in)

Wed, Fri 9:10 - 10:25, CMI Lecture Hall B

(Hyperbolic Tiling VI by Vladimir Bulatov)

Texts:

Geometry of Surfaces by John Stillwell
The Geometries of 3-Manifolds by Peter Scott
Three-dimensional Geometry and Topology by William Thurston

Grading:

Midterm Exam: 25%
Final Project: 25%
Written problem sets: 25%
Class Participation: 25%


Note that this course will be run in a seminar style. Students are expected to do a thorough reading of the assigned topics before each meeting and come prepared to discuss the reading and ask questions. Lecturing will be kept to a minimum, in favor of taking turns at the blackboard explaining the portions we are comfortable with, as we discuss the reading. Students will also be assigned specific proofs and examples to present to the rest of the class. Each week there will be one graded assignment, usually in the form of a problem set to be handed in.

Towards the end of the semester each student will give a presentation (each of which will take up one meeting) of a special topic related to low-dimensional topology. The instructor will work closely with the student in finding an appropriate project. The final exam will be a write-up of this special topic.

Problem sets so far:

Homework #1 due on Wednesday February 03.
Homework #2 due on Saturday February 13.
Homework #3 due on Friday February 19.
Homework #4 due on Wednesday March 09.
Homework #5 due on Wednesday March 23.
Homework #6.

Meeting Schedule:

date topic announcements
jan 20 (wed)       stillwell 1.1 - 1.4            
feb 3 (wed) stillwell 1.5 - 2.3 homework #1 due
feb 4 (thu) stillwell 2.4
feb 10 (wed) stillwell 2.5-2.7
feb 13 (sat) stillwell 2.8-2.10, 3.1 - 3.5 double meeting, homework #2 due
feb 17 (wed) stillwell 3.6 - 3.7
feb 19 (fri) stillwell 3.8 - 4.1 homework #3 due
feb 24 (wed) MIDTERM EXAM WEEK
feb 26 (fri) MIDTERM EXAM WEEK
mar 2 (wed) stillwell 4.2 - 4.4
mar 4 (fri) stillwell 4.5 - 4.6
mar 9 (wed) stillwell 4.7 - 4.10, homework #4 due
mar 11 (fri) stillwell 5.1 - 5.3
mar 16 (wed) stillwell 5.4 - 5.6
mar 18 (fri) stillwell 5.7 - 5.9
mar 23 (wed) stillwell 6.1 - 6.2 homework #5 due
mar 30 (wed) stillwell 6.3 - 6.10
apr 1 (fri) stillwell 7.1 - 7.2
apr 6 (wed) stillwell 7.3 - 7.5
apr 8 (fri) prime decomposition of 3-folds presentation by pranav
apr 13 (wed) intro to teichmuller space presentation by diptaishik
apr 15 (fri) the gauss-bonnet theorem presentation by venkatesh
apr 18 (mon) 8 model geometries part I presentation by nachiketa
apr 20 (wed) on orbifolds & seifert fiber spaces presentation by neetal
apr 22 (fri) 8 model geometries part II presentation by nachiketa
apr 27 (wed) no class FINAL EXAM WEEK
apr 29 (fri) no class FINAL EXAM WEEK

Here is Nachiketa's informative write-up on the 8 model geometries for three-manifolds.

({5,3,4} honeycomb tiling by Roice Nelson)