TOPOLOGY REVIEW-SUMMER 2023


Sessions meet in Ayres 114, 3:30--6:00

Topics and references

The sessions will be `problem seminars': write down solutions to as many problems
as possible from the given sets prior to each meeting, with a view to presenting them
to the other participants for discussion. (Students unable to attend physically: email
your solutions to me on the corresponding date or shortly thereafter, and I will comment
on them.)


M 6/5   General Topology

Problem set 1:  3 , 5, 8, 10, 12, 13 from List 1

and                2(i), 6, 7, 8, 9 from List 2

and                5, 6, 7+8 from  List 3


W 6/7  Compact spaces and proper maps

Problem set 2: 3+4, 6, 8, 9, 10, 11 from List 4
See also: 20, 21, 22, 25, 26, 28


M 6/12 Topology in spaces of maps
Problem set 3: 2, 3, 4, 6, 7, 11, 14, 15, 18, 21 from List 5
Also read:
Arzela-Ascoli notes
Examples: compactness, etc.


W 6/14 Manifolds, immersions, embeddings, transversality
Problem set 4: manifolds



M 6/19  Juneteenth holiday


W 6/21 Homotopy, extensions, approximations
Problem set 5: homotopy


F 6/23 class postponed


M 6/26 Fundamental group, Covering maps, covering spaces
Problem set 6: Fundamental group and covering spaces
Emphasis on problems: 1, 2, 3, 4, 6, 7, 8, 11, 12, 13, 17, 18
(but see also the others, esp. 20, 21, 23, 28, 31, 32, 37, 38)

some solutions

W 6/28 Mod 2 intersection and applications
Problem set 7: mod 2 degree and related
problems 5, 6, 9, 11, 12, 13, 15, 17, 18 from this list

F 6/30 Oriented intersection, degree, applications
Problem set 8: Z-valued degree and related
problems 20, 21, 22, 23, 24, 27, 31, 33, 34 from this list


STUDY GUIDE