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April 2022 Monodromies of splitting families for degenerations of Riemann surfaces
Takayuki Okuda
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Osaka J. Math. 59(2): 315-340 (April 2022).

Abstract

When we study degenerations of Riemann surfaces from a topological viewpoint, the topological monodromies play a very important role. In this paper, as an analogy, we introduce the concept of “topological monodromies of splitting families" for degenerations of Riemann surfaces, and their “monodromy assortments". We show that the monodromy assortments of barking families associated with tame simple crusts act as a pseudo-periodic homeomorphism of negative twist on each irreducible component of the main fibers. As an application of our results, we show an interesting example of two splitting families for one degeneration that have different topological monodromies, although they give the same splitting.

Acknowledgments

The author would like to express his deep gratitude to Professor Osamu Saeki for helpful suggestions and warm encouragement. The author would also like to thank Professors Shigeru Takamura and Tadashi Ashikaga for insightful comments.

The author also thanks the anonymous referee for giving very useful comments on an earlier version of the paper.

Citation

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Takayuki Okuda. "Monodromies of splitting families for degenerations of Riemann surfaces." Osaka J. Math. 59 (2) 315 - 340, April 2022.

Information

Received: 4 December 2017; Revised: 23 December 2020; Published: April 2022
First available in Project Euclid: 7 April 2022

Subjects:
Primary: 14D05 , 32S50
Secondary: 14D06 , 14H15

Rights: Copyright © 2022 Osaka University and Osaka City University, Departments of Mathematics

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Vol.59 • No. 2 • April 2022
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