## Mathematics 338 :  TopologyFall 2022Introduction

Professor:        Jeff Johannes                                    Section 1    MWF    11:30a-12:20p    South 328
Office:            South 326A
Telephone:      245-5403
Office Hours:    Monday 3:30 - 4:30p South 328, Tuesday 8:00 - 9:00p South 336, Wednesday 10:30 - 11:20a South 328, Thursday 4:00 - 5:00p Welles 121, Friday 1:00 - 2:00p South 338, and by appointment or visit.
Web-page:        http://www.geneseo.edu/~johannes

Textbooks
Introduction to Topology, Bert Mendelson
Additional notes provided on-line and in handouts.

Course Goals
• Discuss the fundamentals of general topology (topological spaces, separability, continuous functions, connectedness, and compactness)
• Apply them to the fascinating topics of geometric topology (classification of surfaces and manifolds, knots and links)
• Hint toward more advanced topics in fundamental groups

Learning Outcomes:  Upon successful completion of Math 338 - Topology, a student will be able to:

• Define and illustrate the concept of topological spaces and continuous functions,
• Define and illustrate the concept of product topology and quotient topology,
• Prove a selection of theorems concerning topological spaces, continuous functions, product topologies, and quotient topologies,
• Define and illustrate the concepts of the separation axioms,
• Define connectedness and compactness, and prove a selection of related theorems, and
• Describe different examples distinguishing general, geometric, and algebraic topology.
Your grade in this course will be based on presenting problems in class, problem sets and one research project. Problem sets will be worth 13/20, the project 1/5, and presentations worth 3/20.

Student Presentations
Every two weeks ending on Wednesdays, each student must present at least one problem.  Problems are to be selected from the material for that day's section(s).  Discussing problems with classmates or me is highly endorsed.  Presentations will be scored out of at most 4 points.  The class presentations will be graded roughly as follows:
4    excellent
3.5 very good - at most minor errors
3    some problems, but the main idea of the solution is clear
2    some correct things
1    attempted
0    no presentation
I will determine priority for presenting problems.  Each student who has not yet presented will have priority over students who have presented.  A second (or more) problem may be presented in order to replace a prior presentation.

Problem Sets
Problem sets will consist of 5-10 questions related to material presented in the previous two weeks.  They will be due two weeks after assigned.  They will consist of assigned problems not presented by students in the prior two weeks.  Before these papers are handed  in,  I strongly suggest discussing them with me and others outside of class.   Each problem will be graded on a ten point decile scale based on completeness, accuracy, and writing.
These problems will be evaluated as follows.
0    missing
3    question copied, nothing written
6    something written that appears that it was only written to take up space
7    substantially incomplete.  Something written,  but does not really answer the main questions.  Major errors. Very poor writing
8    mostly complete. maybe a few minor errors
9    complete, no errors, some personal insight, well-written
10  wonderful
No late problem sets will be accepted.

Solutions and Plagiarism
There are plenty of places that one can find all kinds of solutions to problems in this class.  Reading them and not referencing them in your work is plagiarism, and will be reported as an academic integrity violation.  Reading them and referencing them is not quite plagiarism, but does undermine the intent of the problems.  Therefore, if you reference solutions you will receive 0 points, but you will *not* be reported for an academic integrity.  Simply - please do not read any solutions for problems in this class.

Final Project
You will write a 1200-2000 word research paper on a topology topic not covered in class.   Selecting the topic by the deadline will be worth 5%, annotated bibliography will be worth 15%, the draft will be worth 20%, the 10-12 minute presentation will be worth 20%, and the final paper will be worth 40%.

Feedback
Occasionally you will be given anonymous feedback forms.  Please use them to share any thoughts or concerns for how the course is running.  Remember, the sooner you tell me your concerns, the more I can do about them.  I have also created a web-site which accepts anonymous comments.  If we have not yet discussed this in class, please encourage me to create a class code.  This site may also be accessed via our course page on a link entitled anonymous feedback.  Of course, you are always welcome to approach me outside of class to discuss these issues as well.

Accommodations
SUNY Geneseo is dedicated to providing an equitable and inclusive educational experience for all students. The Office of Accessibility will coordinate accommodations, auxiliary aids, and/or services designed to ensure full participation and equal access to all academic programs, activities, and services at SUNY Geneseo. Students with letters of accommodation should submit a letter and discuss needs at the beginning of the semester. Please contact the Office of Accessibility Services for questions related to access and accommodations.  Erwin Hall 22 (585) 245-5112 access@geneseo.edu www.geneseo.edu/accessibility-office.

Religious Holidays
It is my policy to give students who miss class because of observance of religious holidays the opportunity to make up missed work.  You are responsible for notifying me no later than September 12 of plans to observe the holiday.

Military Obligations
Federal and New York State law requires institutions of higher education to provide an excused leave of absence from classes without penalty to students enrolled in the National Guard or armed forces reserves who are called to active duty. If you are called to active military duty and need to miss classes, please let me know and consult as soon as possible with the Dean of Students.

Tentative Schedule subject to change (details will be added as the semester unfolds - check back)

Date              Topic                                                           Assigned                         Due
August 29    Induction, Day 0
31       Day 1, Review M.Chapter 1                        PS1
September 2 M3.1-2 (finish the half-paragraph on p. 73, then skip to Def. 2.4 on p. 74)

7  some M3.3 (just p. 76 starting with "Given two distinct points ending with the paragraph on the top of p. 77, then do read questions 3-4, replacing "neighbourhood" with "open set" )
9 discuss PS1                                                         PS2                                  PS1

12 M3.4 (skip p. 81 and Lemma 4.1 on p. 82)
14 M3.5 (skip the top of page 88, before Theorem 5.3, which we will use as a definition; therefore skip its proof)
16 M3.6

19 M3.7                                                                                                           Project Topic
21 M3.8
23 discuss PS2                                                     PS3                                   PS2

26 C1.1,4
28 C2.1,2
30 discuss PS3, C3.1,2                                         PS4                                    PS3

October 3 C3.2,3
5 C3.4
7 C4.1

12 M4.2
14 M4.3, 4.4                                                                                                 Annotated Bibliography

17 discuss PS4                                                     PS5                                 PS4
19 M4.5, 4.6
21 replanning

24 discuss PS5                                                    PS6                                PS5
26 M5.2
28 M5.3, 5.4

31 discuss PS6 - choice
November 2 Manifolds
4 M4.7

7 discuss PS7     M4.7/8?                                  PS7                                PS6
9  M4.8
11                                                                                                              Project Draft

14
16
18

21 discuss PS7                                                PS8                                PS7

28
30
December 2

5
7
9 discus PS8                                                                                          PS8

12                            Project Paper due

Thursday, December 15    8:30 - 11a   Project presentations