Construction of biordered sets from vector bundles (Q5926763)

Starting from the point of view that the biordered sets of the semigroups of the type \((X, F(H))\), (the set of all continuous maps from a compact Hausdorff space \(X\) to the set \(F(H)\) of all Fredholm operators on the infinite-dimensional Hilbert space \(H\)) can be described in a more general way in terms of vector bundles, the author constructs here biordered sets from two collections \(C\) and \(C'\) of vector bundles, where \(C\) is a class of vector bundles of finite-dimensional subspaces of \(H\) and \(C'\) is a class of vector bundles of finite codimensional subspaces of \(H\), all over \(X\) (the relation between vector bundles and semigroup of Fredholm operators with a parameter has been discussed in a previous paper of \textit{L. John} and \textit{A. R. Rajan}, Bull. Calcutta Math. Soc. 86, No. 4, 335-348 (1994; Zbl 0879.47019)).