91 research outputs found
Homotopy excision and cellularity
Consider a push-out diagram of spaces C B, construct the homotopy
push-out, and then the homotopy pull-back of the diagram one gets by forgetting
the initial object A. We compare the difference between A and this homotopy
pull-back. This difference is measured in terms of the homotopy fibers of the
original maps. Restricting our attention to the connectivity of these maps, we
recover the classical Blakers-Massey Theorem.Comment: 22 pages, we took special care in this revised version in
distinguishing fiber sets from single fibers, in indicating what we mean by
the loop space on a possibly non-connected and unpointed space, thus
smoothing the expositio
Topological computation of some Stokes phenomena on the affine line
Let be a holonomic algebraic -module on the affine
line, regular everywhere including at infinity. Malgrange gave a complete
description of the Fourier-Laplace transform , including
its Stokes multipliers at infinity, in terms of the quiver of . Let
be the perverse sheaf of holomorphic solutions to . By the
irregular Riemann-Hilbert correspondence, is determined
by the enhanced Fourier-Sato transform of . Our aim here is
to recover Malgrange's result in a purely topological way, by computing
using Borel-Moore cycles. In this paper, we also consider some
irregular 's, like in the case of the Airy equation, where our
cycles are related to steepest descent paths.Comment: 50 pages, to appear at Annales de l'Institut Fourier, v3: some minor
(editorial) correction
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