镜像五次三重中拉格朗日子流形的同调支撑
Homology supported in Lagrangian submanifolds in mirror quintic threefolds
摘要：
本文研究了镜像五次Calabi-Yau三重空间中的同调圈，它可以由特殊的拉格朗日子流形实现。我们利用Picard-Lefschetz理论建立了单值作用量，并研究了拉格朗日消失环的轨道。对于许多素数$p$，我们可以计算轨道模$p$。我们猜想，与$\mathbb{Z}$中的系数同调的轨道可以由这些与$\mathbb{Z}_p$中的系数同调的轨道来确定.
英文摘要：
In this note we study homological cycles in the mirror quintic Calabi-Yau threefold which can be realized by special Lagrangian submanifolds. We have used Picard-Lefschetz theory to establish the monodromy action and to study the orbit of Lagrangian vanishing cycles. For many prime numbers $p$ we can compute the orbit modulo $p$. We conjecture that the orbit in homology with coefficients in $\mathbb{Z}$ can be determined by these orbits with coefficients in $\mathbb{Z}_p$.
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