Discrete monopoles and instantons over projective spaces

✍ Scribed by Thomas W. Kephart; Tzu Chiang Yuan

• Publisher: Springer
• Year: 1991
• Tongue: English
• Weight: 403 KB
• Volume: 21
• Category: Article
• ISSN: 0377-9017
• DOI: 10.1007/bf00398328

✦ Synopsis

We generahze Manton's construction of discrete monopoles in Minkowski space to their analog m CP(n), Topological charge, analogous to the first Chern number in the smooth bundle, is obtained for the corresponding discrete bundle and is shown to be Q = +1. We also discuss the &scretizatlon of the smooth sphere bundles over the real projective space RP(n) and the quaternionic projective space HP(n). Finally, we make a conjecture of the discretization of the smooth sphere bundles over the discrete projecUve spaces R2kP(n) for all positive integers k and n.

AMS subject classification (1980). 55R25. * The smooth spaces R~'P(n) exist only for k = 0, 1 and 2 with n a positive integer, and for k = 3 only n = 1 or 2. These are the smooth projective spaces RP(n), CP(n), HP(n), OP(1), and OP(2). The discrete projective spaces have no such restriction.