Open Access
June 2017 One-parameter Families of Homeomorphisms, Topological Monodromies, and Foliations
Kenjiro SASAKI
Tokyo J. Math. 40(1): 65-81 (June 2017). DOI: 10.3836/tjm/1502179216


The homological monodromy of a degeneration whose singular fiber has at most normal crossings was described by C. H. Clemens. In his work, local monodromies were described in detail. It is actually a classical result that the local monodromy around a node is a Dehn twist. For higher-dimensional case, we describe local monodromies alternatively: On a local smooth fiber of dimension $n \geq 2$, we construct $n+1$ singular foliations and then describe the action of the local monodromy on each leaf. Here the $i$th singular foliation is used for describing its action on the $i$th face of the boundary of a local smooth fiber.


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Kenjiro SASAKI. "One-parameter Families of Homeomorphisms, Topological Monodromies, and Foliations." Tokyo J. Math. 40 (1) 65 - 81, June 2017.


Published: June 2017
First available in Project Euclid: 8 August 2017

zbMATH: 1376.32015
MathSciNet: MR3689979
Digital Object Identifier: 10.3836/tjm/1502179216

Primary: 32G05

Rights: Copyright © 2017 Publication Committee for the Tokyo Journal of Mathematics

Vol.40 • No. 1 • June 2017
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