Pointed harmonic volume and its relation to the extended Johnson homomorphism
Pointed harmonic volume and its relation to the extended Johnson homomorphism
复制标题
尖调和体积及其与扩展约翰逊同态的关系
DOI：
10.1142/s1793525319500407
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发表时间：
2020
影响因子：
0.8
通讯作者：
Yuuki Tadokoro
中科院分区：
文献类型：
--
作者：
Sano Yuji;Takeyoshi Kogiso;Yuji Sano;Yuji Sano;Takeyoshi Kogiso;Yuji Sano;Takeyoshi Kogiso;小木曽岳義;Yuji Sano;Yuji Sano;小木曽岳義;Yuji Sano;Yuuki Tadokoro
紧致黎曼曲面的周期由微分1-形式的积分定义，是经典的复解析不变量，与曲面的复杂结构密切相关。在本文中，我们处理另一个复杂的解析不变量称为尖调和体积。作为使用Chen迭代积分定义的周期的自然扩展，它捕获了复杂结构的更详细的信息。它也是复杂解析不变量的少数几个明确可计算的例子之一。对于一类尖超椭圆曲线，我们得到了它的新值。给出了尖调和体积的一个应用。本文给出了点定向闭曲面的映射类群上调和体积与第一扩张约翰逊同态之间的关系。此外，我们明确地计算了这种同态的一定限制。
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 paper, 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. Moreover, we explicitly compute a certain restriction of this homomorphism.