Math 6310: Topology

 

Spring 2024

 

SCI 3.240 / TTh 2:30 - 3:45pm

 

Instructor:

Baris Coskunuzer / coskunuz@utdallas.edu

 

 

Office Hours:

BC: Tu 1-2:15pm at FA 2.410.†††† AT: Wed 3-5pm at FO 1.210.

 

 

Textbooks:

Algebraic Topology by Allen Hatcher

 

 

Prerequisites:

Math 5301 or consent of the instructor.

 

 

Content

Elements of Algebraic Topology, Fundamental Group, Homology.

 

 

Homework:

HWs are assigned weekly and due Thursday class. HW with the lowest score will be dropped.

 

 

Exams:

There will be 2 in-class exams on March 7 and Apr 18. Final Exam TBA.

 

 

Grading:

HW 25% + Midterm Exams 20% each + Final Exam 35%

 

Weekly Schedule and HW Assignments:

Week of

Topics

HW Problems

HW due

Jan 15*

Ch 0. Intro + Basics of Topology

No HW due to cancelled class.

Jan 22

Ch 0. Homotopy & Cell Complexes

HW1: Ch-0. 1, 2, 3, 4, 9, 10, 12* (PC only).

Feb 1

Jan 29

Ch 1.1 Fundamental Group

HW2: Ch-0. 14, 16, 19, 20, 23.

Feb 8

Feb 5

Ch 1.2 Van Kampenís Thm

HW3: Ch-1.1  1, 2, 5, 8, 16a, 16d, 16f.

Feb 15

Feb 12

Ch 1.3 Covering Spaces

HW4: Ch-1.2  3, 4, 7, 8, 10.

Feb 22

Feb 19

Ch 1.3 Covering Spaces

HW5: Ch-1.3 1, 4, 5, 8, 10.

Feb 29

Feb 26

Ch 2 Homology Intro

Mar 4

Review + Midterm 1

 

Mar 18

Ch 2.1 Simplicial Homology

HW6: posted in Elearning

Mar 28

Mar 25

Ch 2.2 Singular Homology

HW7: posted in Elearning

Apr 4

Apr 1

Ch 2.2 Cellular Homology

HW8: posted in Elearning

Apr 11

Apr 8

Ch 2.3 Homology Theory

 

Apr 18

Apr 15

Review + Midterm 2

 

 

Apr 22

Ch.3 Cohomology Overview

 

May 1

Apr 29

Applications & Review

 

 

 

 

 

 


 

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