Title : Graphic calculus of monodromy representations of topological objects
Speaker : Seiichi Kamada (Hiroshima University)
Abstract :

Monodromy representations often classify and bring us a lot of information for various topological objects; $2$-dimensional braids, knotted surfaces in $4$-space in braid forms, Lefschetz fibrations of $4$-manifolds, algebraic curves, hyperplane arrangements, etc. However it is usually hard to classify the monodromy representations or even to decide whether two given representations are isomorphic or not. Here we introduce a method to describe monodromy representations for the topological objects, or any $G$-monodromy representations, by use of graphics, called {\it charts\/}. We would also like to introduce some recent results on $2$-dimensional braids and Lefschetz fibrations that are collaborated with Y. Matsumoto, T. Matumoto and K. Waki.

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