## Fibring spaces of maps: Fredholm structures |

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Annals of Math Banach Lie Banach space bijective bounded subsets bundle map C^-trivial fibration Cartan characteristic classes classifying space closed subset codimensional cohomology compact map compact-open topology continuous map contractible cp(x Cr-manifold defined diagram diffeomorphisms differential dimensional Hilbert space embedding evaluation map Example fibre bundles filtration finite dimensional Finsler structure flag foliation Fredholm bundle map Fredholm map Fredholm operator Fredholm reduction Fredholm structure Fredholm submanifold Furthermore G-bundle GC(E GL(E GL(E)-bundle group G Gysin homomorphism Hilbert space homology homotopy classes homotopy equivalence homotopy groups homotopy theorem identity component inclusion map induces infinite dimensional Hilbert Lefschetz Lie group locally C°-trivial fibration locally compact locally trivial fibration LPC(E map cp metric modeled natural map open subset oriented Fredholm manifolds p,qv paracompact space principal bundle proper quotient separable Hilbert space separable infinite dimensional sequence Serre Smale subgroup Suppose surjective topological group transversal Tromba University vector bundle