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Studying complex manifolds by using groups $G_{n}^{k}$ and $Γ_{n}^{k}$

Vassily Olegovich Manturov

Moscow Institute of Physics and Technology, Moscow 105005, Russia

Northeastern University, Shenyang City, Liaoning Province, People’s Republic of China

Kazan Federal University, Kazan, Russia

E-mail Address: vomanturov@yandex.ru

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and

Zheyan Wan

Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, P. R. China

E-mail Address: wanzheyan@mail.tsinghua.edu.cn

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https://doi.org/10.1142/S0218216520430026Cited by:0 (Source: Crossref)

This article is part of the issue:

Special Issue: Moscow-Beijing Conference on Topology
Guest Editors: Z. Wan, S. Ren and V. O. Manturov

Abstract

In this paper, we study several complex manifolds by using the following idea. First, we construct a certain moduli space and study the fundamental group of this space. This fundamental group is naturally mapped to the groups $G_{n}^{k}$ and $Γ_{n}^{k}$ . This is the step towards “complexification” of the $G_{n}^{k}$ and $Γ_{n}^{k}$ approach first developed in [V. O. Manturov, D. A. Fedoseev, S. Kim and I. M. Nikonov, On groups $G_{n}^{k}$ and $Γ_{n}^{k}$ : A study of manifolds, dynamics, and invariants, preprint (2019), arXiv:1905.08049].

Keywords:

AMSC: 51H20, 20F36, 57M25, 57M27

References

1. D. A. Fedoseev, I. M. Nikonov and V. O. Manturov, Manifolds of Triangulations, braid groups of manifolds and the groups $Γ_{n}^{k}$ , preprint (2019), arXiv:1912.02695. Google Scholar
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