Find Paper, Faster
Example:10.1021/acsami.1c06204 or Chem. Rev., 2007, 107, 2411-2502
A fibration theorem for collapsing sequences of Alexandrov spaces
Journal of Topology and Analysis  (IF0.457),  Pub Date : 2021-03-22, DOI: 10.1142/s179352532150028x
Tadashi Fujioka

Suppose a sequence Mj of Alexandrov spaces collapses to a space X with only weak singularities. Yamaguchi constructed a map fj:MjX called an almost Lipschitz submersion for large j. We prove that if Mj has a uniform positive lower bound for the volumes of spaces of directions, which is sufficiently large compared to the weakness of singularities of X, then fj is a locally trivial fibration. Moreover, we show some properties on the intrinsic metric and the volume of the fibers of fj.