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Introduction for topology

  1. Jan 6, 2012 #1
    i studied Sadri Hassani az mathematical physics book.
    if i want to learn topology (( for general relativity )) what it the best book for introduction ?
  2. jcsd
  3. Jan 6, 2012 #2


    Staff: Mentor

  4. Jan 7, 2012 #3


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    mathematicians will beat me but I like Nakahara "Geometry, topology and physics"; it has something to say about spacetime (differential) topology, Riemannian & Kähler manifolds, but in addition it focusses on gauge theories and fibre bundles
  5. Jan 8, 2012 #4
    Most purely topology books will spend a lot of time being useless to GR. The intro books cover mostly just general topology. I like Gamelin and Greene and it is pretty cheap. It starts with metric spaces and finishes with a bit of algebraic topo. Kasriel's Undergraduate Topology gets good reviews, but I didn't really like it. The best is Munkres, but it is expensive and hard to get into unless you are in a class or very dedicated to topology.

    You may want to skip general topology unless you want to learn it in general for fun. I took a general topology (point-set topology) class that spent the last two weeks with an intro to algebraic topology. I am glad I took the class, but most topo of interest to physics is algebraic, and most topology books spend a lot of time on general topology.

    So, my opinion, is Gamelin and Greene Intro to Topology for an inexpensive reference for general topology ideas without as much detail as an Analyst would want, and a physics book with more algebraic topology.
  6. Jan 8, 2012 #5

    George Jones

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    Which book, Mathematical Methods for Students of Physics and Related Fields, or Mathematical Physics: A Modern Introduction to Its Foundations?
    Do you want to learn topology because: 1) you think that some knowledge of topology is necessary prior to learning general relativity; or 2) you have seen topological arguments used is general relativity, for example, in Hawking and Ellis; or 3) of some other reason?
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