2012/08/29 by Mathieu Anel, Adam Clay, Anel, Mathieu +1
Mathematics · #06F15 #20F60 #57M10 #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR) #math.AT #math.GR #msc:06F15 #msc:20F60 #msc:57M10
paper · pdf · doi:10.48550/arxiv.1208.5844
13 pages
arxiv created 2012/08/29 · arxiv updated 2012/08/30
We define what is meant by a strict total order in a category having subobjects, products and fibre products. This allows us to define the notions of an ordered bundle X and an ordered G-set; when G=π1(X) we relate these structures to orderings of π1(X). We apply this to prove a theorem of Farrell relating right-orderings of π1(X) to embeddings of the universal cover into line bundles over X, and generalize it by relating bi-orderings of π1(X) to embeddings of the path space into line bundles over X × X.