In: Klein, P.N. (ed.) Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017, Barcelona, Spain, Hotel Porta Fira, January 16–19, pp. 2733–2747. Society for Industrial and Applied Mathematics, USA (2017). https://doi.org/10.1137/1.9781611974782.181...
There is a canard that every textbook of algebraic topology either ends with the definition of the Klein bottle or is a personal communication to J. H. C. ... JJ Rotman - PERGAMON 被引量: 707发表: 1957年 A generating function for the Euler characteristic of out(Fn) Let A be a group...
For example, if one computes the homology of the Klein bottle (see Section 7.1.1) with coefficients in the field Fp with p elements, where p is a prime, then β0(K)=1 for all primes p. However, β1(K)=2 and β2(K)=1 if p=2, but β1(K)=1 and β2(K)=0 for all ...
sidedsurfacethat is closed, that is, without any one-dimensional boundaries. This example, now called theKlein bottle, cannot exist in three-dimensional space without intersecting itself and, thus, was of interest to mathematicians who previously had considered surfaces only in three-dimensional space...