Realizability of a braid monodromy by an algebraic function in a disk |
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| Institution: | 1. System Studies Institute, Russ. Acad. Sci. Avtozavodskaya 23, Moscow, Russia;2. Laboratoire de mathématiques pures de Bordeaux, université Bordeaux I, 351, cours de la Libération, 33405 Talence cedex, France;1. School of Mathematics, Hangzhou Normal University, Hangzhou 311121, PR China;2. Department of Mathematics-Computer Sciences, Necmettin Erbakan University, Konya, Turkey;3. Institute de Mathématiques, Université Bourgogne Franche-Comté, Dijon, France;1. Median Technologies, Valbonne, France;2. Inserm UNIS UMR1072, Université Aix-Marseille AMU, Marseille, France;1. School of Psychological Sciences and Turner Institute for Brain and Mental Health, Monash University, Melbourne, Victoria, Australia;2. Center for Information and Neural Networks (CiNet), National Institute of Information and Communications Technology (NICT), Suita, Osaka 565-0871, Japan;3. Advanced Telecommunications Research Computational Neuroscience Laboratories, 2-2-2 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-0288, Japan;4. National Institute of Advanced Industrial Science and Technology, Tsukuba 305‐8566, Japan;5. Nagahama Institute of Bio-Science and Technology, 1266 Tamura-cho, Nagahama, Shiga 526-0829, Japan;1. Department of Mathematics, Montana State University, Bozeman, MT 59717, United States;2. Department of Mathematics, Northwestern University, Evanston, IL 60208, United States;3. Department of Mathematics, Harvard University, Cambridge, MA 02138, United States;1. INL – International Iberian Nanotechnology Laboratory, Braga, Portugal;2. University of Edinburgh, United Kingdom |
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| Abstract: | A braid is called algebraic if it is conjugated to the local braid of an algebraic function at a singular point. It is shown that any homomorphism of a free group into a braid group which takes each generator to an algebraic braid, can be realized as the braid monodromy of an algebraic function in a disk. |
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