Abstract
The problem of finding full automorphism groups of compact Riemann surfaces is classical, though complete results are only known for a few families. One tool used in some classification schemes is strong branching; a condition derived by Accola in [1]. In the following, we survey the main ideas behind strong branching including a general survey of current results. We also provide new results for families for which we can find the full automorphism group using strong branching and an inductive version of strong branching.
Acknowledgement
This work was initiated with Kay Magaard at the BIRS workshop “Symmetries of Surfaces, Maps and Dessins” in September 2017. The authors are grateful to Kay for sharing his deep insight into the problem, especially introducing us to works [2], [13] and [16] (of which he is a coauthor), and we dedicate this work to his memory. We would also like to thank BIRS, and the organizers of the workshop for providing us a beautiful venue to work on this project together.
Dedication
Dedicated to the memory of Kay Magaard
Citation
S. Allen Broughton. Charles Camacho. Jennifer Paulhus. Rebecca R. Winarski. Aaron Wootton. "USING STRONG BRANCHING TO FIND AUTOMORPHISM GROUPS OF -GONAL SURFACES." Albanian J. Math. 12 (1) 89 - 129, 2018. https://doi.org/10.51286/albjm/1548957804
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