On the fundamental group of a space of sections.
Following a Bendersky-Gitler idea, we construct an isomorphism between Anderson’s and Arone’s complexes modelling the chain complex of a mapping space. This allows us to apply Shipley’s convergence theorem to Arone’s model. As a corollary, we reduce the problem of homotopy equivalence for certain “toy” spaces to a problem in homological algebra.
Let be the universal connection on the bundle . Given a principal -bundle with connection , we determine the homotopy type of the space of maps of into such that is isomorphic to . Here denotes pull-back.
Si esamina la successione spettrale per la -coomologia dello spazio totale di un fibrato olomorfo nel caso in cui le fibre siano varietà di Stein.