Induced Topology on the Hoop Group
نویسندگان
چکیده
A new topology is proposed on the space of holonomy equivalence classes of loops, induced by the topology of the space Σ in which the loops are embedded. The possible role for the new topology in the context of the work by Ashtekar et al. is discussed. In this short paper we introduce a topology τ on the space of holonomy equivalence classes of loops, known in the context of quantum gravity in the Ashtekar variables as the hoop group HG. The first section is devoted to notation by introducing hoops etc. The main part is the second section in which the topology is defined. In the last section we briefly discuss how this topology might be of interest for the work by Ashtekar et.al. [1] [2] regarding the non-linear functional analysis of the quotient space of connections modulo gauge transformations A/G.
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