2013/05/07 by Daciberg Lima Gonçalves, Daciberg L. Gonçalves, Gonçalves, Daciberg L. +2
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:55M20 #msc:55R05 #msc:55S35 #msc:57R19 #msc:57R90
paper · pdf · doi:10.48550/arxiv.1305.1650
coincidence, fixed point, map over B, normal bordism, ω-invariant, Nielsen number, Reidemeister class, Dold's index, fibration
arxiv created 2013/05/07 · arxiv updated 2013/05/09
Let M to B, N to B be fibrations and f1,f2 :M to N be a pair of fibre-preserving maps. Using normal bordism techniques we define an invariant which is an obstruction to deforming the pair f1,f2 over B to a coincidence free pair of maps.In the special case where the two fibrations are the same and one of the maps is the identity, a weak version of our ω-invariant turns out to equal Dold's fixed point index of fibre-preserving maps. The concepts of Reidemeister classes and Nielsen coincidence classes over B are developed. As an illustration we compute e.g. the minimal number of coincidence components for all homotopy classes of maps between S1-bundles over S1 as well as their Nielsen and Reidemeister numbers.