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