Which Textbook for Studying Homotopy is Best for Beginners?

  • Context: Graduate 
  • Thread starter Thread starter homology
  • Start date Start date
  • Tags Tags
    Studying Textbook
Click For Summary

Discussion Overview

The discussion revolves around recommendations for textbooks suitable for beginners studying homotopy, particularly in the context of supplemental materials to Munkres' Topology. Participants share their experiences and suggest alternatives that may provide clearer explanations or a more accessible approach to the subject.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant mentions studying homotopy using Munkres' Topology but finds certain concepts challenging, such as free groups and the fundamental group.
  • Another participant suggests Andrew Wallace's book on algebraic topology as a more accessible text, noting its clarity and user-friendliness.
  • A later reply acknowledges the clarity of Munkres but expresses occasional difficulty with rigor, indicating a need for supplementary resources.
  • There is a mention of another book by Wallace that covers covering spaces and classification of compact surfaces, although the participant is uncertain if it is indeed by Wallace.

Areas of Agreement / Disagreement

Participants generally agree that Munkres is a clear text, but there is no consensus on the best supplemental text, as different suggestions are made and experiences vary.

Contextual Notes

Some participants express uncertainty about the specific titles and contents of Wallace's books, indicating a need for further verification of their relevance and clarity for beginners.

Who May Find This Useful

Readers interested in studying homotopy, particularly those seeking beginner-friendly resources or supplemental materials to standard texts.

homology
Messages
305
Reaction score
1
Hello,

I've been studiing homotopy this semester in a readings course out of Munkres Topology book. I'm in the mismash about free groups, wedgies of circles and pasting stuff. Could you recommend a lower level text that I could peruse as a supplemental text? Something a bit more explicit for those times when I'm dumber than usual.

Your responses are appreciated, thank you...

homology
 
Physics news on Phys.org
well munkres is usually considered about as explicit and user friendly as books come, but there is a lower level book on the first homotopy group, i.e. the "fundamental group", that i started on and appreciated very much as a college student. It is by Andrew Wallace, and all his books are written to be understood.

this might be it, but it would be wise to search in your library.

Wallace, Andrew H.
Algebraic Topology: International Series of Monographs in Pure and Applied Mathematics
Pergamon Press, 1957 Good/No Jacket. Slight signs of wear. Paperclip embossment to front endpapers. Binding is Cloth.
Bookseller Inventory #000130


Price: US$ 22.00 (Convert Currency)
Shipping: Rates & Speed

Bookseller: Black Oak Books 2, ABAA, 630 Irving Street, San Francisco, CA, U.S.A., 94122
(Search this Bookseller's Books) (More Bookseller Information)

Terms of Sale: Shipping: $7.00 1st book within U.S. (UPS Ground-trackable and automatically insured up to $100.00.) Each additional book is $2.50. Media mail & other alternatives are available. Shipping outside U.S.: Costs vary. We ship USPS Global Priority or via air or surface parcel post; other alternatives available. Please specify the method of shipment, or speed of shipment you would prefer. We ship Tuesdays, Thursdays, and Fridays. Checks, Visa, Mastercard, Discover, American Express.

We welcome phone calls at 415-564-0877 between the hours of 10am and 5pm Pacific time. At other times call our order line at 415-564-0879.
Shipping Terms: Shipping costs are based on books weighing 2.2 LB, or 1 KG. If your book order is heavy or oversized, we may contact you to let you know extra shipping is required.

Accepted Payment Methods:
- Visa
- MasterCard
- American Express
- Discover
- Cheque
- Money Order
 
Thanks, my library has a copy so I'll check that out tomorrow. You're right Munkres is pretty clear, however every once and a while I get the rigor-blues.

Thanks,

Homology
 
wallace has another book, a more recent one with covering spaces and classification of compact surfaces as well as fundamental groups. at elast i thinkj that was wallace, but this one is the one i started on.
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 10 ·
Replies
10
Views
5K
  • · Replies 14 ·
Replies
14
Views
6K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 10 ·
Replies
10
Views
5K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 25 ·
Replies
25
Views
4K
  • · Replies 11 ·
Replies
11
Views
4K
  • · Replies 3 ·
Replies
3
Views
6K