Which Textbook for Studying Homotopy is Best for Beginners?

In summary, The conversation is about a student seeking a lower level text on homotopy as a supplement to Munkres' book. The expert suggests a book by Andrew Wallace that is more accessible and user-friendly. The student will check it out tomorrow as their library has a copy. The expert also mentions another book by Wallace that covers topics on covering spaces and classification of compact surfaces.
  • #1
homology
306
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
 
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  • #2
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.
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  • #3
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
 
  • #4
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.
 

FAQ: Which Textbook for Studying Homotopy is Best for Beginners?

What is homotropy?

Homotropy is a mathematical concept that describes the continuous transformation of one mathematical object into another. It is often used in topology to study the properties of spaces and maps between them.

What is the importance of studying homotropy?

Studying homotropy allows us to understand the structure and properties of spaces, and how they can be transformed into each other. This has important applications in various fields such as physics and engineering.

What are some common techniques used in studying homotropy?

Some common techniques used in studying homotropy include the use of homotopy groups, homotopy equivalences, and the homotopy extension property. These techniques allow for the comparison and classification of spaces based on their homotopy properties.

How is homotropy related to other mathematical concepts?

Homotropy is closely related to other mathematical concepts such as homology, cohomology, and category theory. It is also a fundamental part of algebraic topology and has connections to differential geometry and algebraic geometry.

What are some real-world applications of homotropy?

Homotropy has applications in various fields such as physics, engineering, and computer science. It is used to study the behavior of physical systems, design efficient networks, and develop algorithms for data analysis and machine learning.

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