Does anyone know of a book with a chapter explaining fundamental polygons?

By Fundamental Polygon I mean for example, Fundamental polygon of Klein Bottle, as shown below.

I understand it is a pretty basic concept, so most topology books already assume you know it (e.g. Hatcher), and only give a brief explanation to it.

The greatest problem I have with fundamental polygons is edge identifications and "cutting and gluing", as I lack exposure to these concepts and have problems visualising (and knowing what exactly to do). This results in inability to do questions like (Hatcher question: How to Cut and Glue from Tetrahedron to Klein Bottle) which are supposed to be very basic.

Thanks for your help!

enter image description here

  • 1
    $\begingroup$ Maybe one of Massey's books on algebraic topology should help $\endgroup$ – Thomas Rot Jun 1 '16 at 13:51
  • 1
    $\begingroup$ Stillwell's book "Classical Topology and Combinatorial Group Theory" is great. Also, to do these problems with confidence (and rigor) one needs to understand quotient maps and the quotient topology, which you can get in Stillwell's book or in Munkres "Topology". $\endgroup$ – Lee Mosher Jun 1 '16 at 15:03

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.