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
Suppose a sequence $Mj$ of Alexandrov spaces collapses to a space $X$ with only weak singularities. Yamaguchi constructed a map $fj:Mj→X$ 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 $fj$.