labelling points of S2 as orders of the zeroes or poles of a nonzero rational function on the Riemann sphere. This data determines the rational function up to a nonzero scalar multiple. Exercise 17. Give a `particle picture ' of points in EG similar to that for BG. (Hint: the big dierence is th...
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| Online Access: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.648.3921 http://math.ucr.edu/home/baez/calgary/calgary_big.pdf |
| Summary: | labelling points of S2 as orders of the zeroes or poles of a nonzero rational function on the Riemann sphere. This data determines the rational function up to a nonzero scalar multiple. Exercise 17. Give a `particle picture ' of points in EG similar to that for BG. (Hint: the big dierence is that now charge is conserved even at the north pole.) Use this to explicitly describe the map G: EG! BG. Show that this is a principal G-bundle. Exercise 18. Dene a concept of `equivalent ' topological categories that gener-alizes the usual notion of equivalent categories. Show that if C and C 0 are equiv-alent topological categories, the spaces jN(C)j and jN(C 0)j are homotopy equiva-lent. Show that the topological category GTor is equivalent to the topological cat-egory with just one object and one morphism. Conclude that EG = jN(GTor)j is contractible. Exercise 19. Show that for any topological group G, BG is connected. Exercise 20. Using the previous two exercises, show that |
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