MAT 530: Topology & Geometry, I

Stony Brook            Fall 2005

 

Announcements

The textbook for MAT 531 next term will be Frank Warner's Foundations of Differentiable Manifolds and Lie Groups, GTM 94. It should be available at the Stony Brook bookstore by the beginning of the semester. It is available on amazon at a discount, with free shipping. Currently, and likely through the end of December, it is also available directly from Springer at an even higher discount. Please do not wait weeks into the semester to acquire the book.

We should be able to cover Chapters 1,2,4,5 and perhaps 6.

 

Handouts

Detailed solutions to the final exam
Notes on Van Kampen's Theorem, with pictures
Detailed solutions to the midterm
Gabriel's solutions to the first problem set, minus the Kuratowski problem, p101 #21

Detailed solutions to:

PS1: p101 #21    PS2: p127 #8    PS3: p158 #12; p178 #5
PS4: p67 #7; p235 #1,5    PS5: p200 #9; p213 #5; p223 #3    PS6: p260 #2,7
PS7: p271 #10; p272 #2    PS8: p335 #4,5; p341 #3    PS9: p353 #4; p359, #4; p366, #9   
PS10: p483 #2,5; p493 #5    PS11: p433 #2; p438 #5; p441 #3; p445 #2    PS12: p454 #3,4; p457 #4; p470 #1

Here are the homework assignments, the course summary, the midterm, the final exam, and the notes on the Fundamental Group and Covering Spaces from last year, prepared by Vladlen Timorin.

 

Course Instructor

Name: Aleksey Zinger     E-mail: azinger@math     Phone: 432-8618
Office: Math Tower 3-117     Office Hours: Mon 130-230 and Wed 3-4

 

Daily Schedule and Homework Assignments

Date Topic Read Problem Set
Aug 29Topological Spaces1-4,12-14 p39 #5; p83 #4,7,8
p92 #3,4,8,10; p100 #7,9,11,21
p111 #2,3,6,12
Aug 31Induced Topologies5,15-17
Sep 2Continuous Functions18,19
Sep 5No Class
Sep 7Product and Quotient Topologies19,22 p118 #6,7; p144 #3,4
p126 #3,5,8; p133 #2,4,6,7
Sep 9Metric Spaces20,21
Sep 12Connectedness and Path-Connectedness23,24 p152 #8,10
p157 #1,2,3,8,12; p162 #2
p170 #1,4,8; p177 #1,5
Sep 14Components and Path-Components9,10,25
Sep 16Compactness26,27
Sep 19Compactness for Metric/Order Topologies 27,28p67 #7; p72 #8
p181 #1,3,7
p186 #4,6; p235 #1,5
Sep 21One-Point Compactification29
Sep 23Tychonoff Theorem11,37
Sep 26Countability and Separation Axioms 30,31 p194 #5,6; p199 #2,4,9
p205 #1,4; p213 #5,7
p218 3,9; p223 #2,3; p227 #5
Sep 28Urysohn Lemma32,33
Sep 30Tietze Extension Theorem35,36
Oct 7Urysohn Metrization Theorem34
Oct 3,5No Class
Oct 10Locally Finite Collections 39,40 p248 #5,6; p252 #3,4
p260 #2,7; p262 #2
Oct 12Nagata-Smirnov Metrization Theorem40,41
Oct 14Smirnov Metrization Theorem41,42
Oct 17Function Spaces 43,44 p271 #7,10; p274 #2
p280 #2; p288 #3,4
p292 #1; p299 #7
Oct 19Compactness in Function Spaces45,46
Oct 21Ascoli's Theorem46,47
Oct 24Baire Spaces48,49
10/26Review
10/28Midterm
Oct 31Path Homotopies 51 p330 #3; p335 #4,5,6
p341 #3,5; p348 #4,6
Nov 2The Fundamental Group52,53
Nov 4The Fundamental Group of S153,54
Nov 7Applications 55 p353 #2,4; p359 #3,4
p366 #7,9; p370 #4
Nov 9More Applications56,57
Nov 11Properties of the Fundamental Group58,59
Nov 14Fundamental Groups of Some Spaces 60 p375 #2,4,5
p483 #2,3,5
p493 #2ab,4,5
Nov 16Equivalence of Covering Spaces79,80
Nov 18Deck Transformations80,81
Nov 21Construction of Covering Spaces81
Nov 23Construction of Covering Spaces (cont'd) 82 p433 #1,2; p438 #2,5
p441 #1,3; p445 #1,2
11/25No Class
Nov 28van Kampen's Theorem67-70
Nov 30Applications71,72,73
Dec 2Surfaces and Decorated Polygons 73,74 p454 #3,4,5; p457 #4
p462 #2; p470 #1; p476 #5
Dec 5Abelianization of Fundamental Group75,76
Dec 7Equivalence Operations76,77
Dec 9Classification of Surfaces77,78
12/12Review
12/19Final Exam, 2-4:30pm
 

This page is maintained by Aleksey Zinger.
Last modified: December 20, 2005.