## 幾何学コロキウム：Pointed harmonic volume and its relation to extended Johnson homomorphism（田所勇樹 氏，木更津工専）

2018年 　 7月 27日 16時 30分 ～ 　 18時 00分

Abstract：
The period for a compact Riemann surface, defined by the integral of differential 1-forms, is a classical complex analytic invariant, strongly related to the complex structure of the surface. In this talk, we treat another complex analytic invariant called the pointed harmonic volume. As a natural extension of the period defined using Chen's iterated integrals, it captures more detailed information of the complex structure. It is also one of a few explicitly computable examples of complex analytic invariants. We obtain its new value for a certain pointed hyperelliptic curve. An application of the pointed harmonic volume is presented. We explain the relationship between the harmonic volume and first extended Johnson homomorphism on the mapping class group of a pointed oriented closed surface.

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