PreprintCC0arXiv
Generalizations of the groups Gnk: graphs, moduli spaces, algebraic geometry, spherical braids
Abstract
In this work, we construct a generalization of the Gnk-theory to the case of an arbitrary hypergraph. The case of spherical braids is considered separately, using the stratification of the moduli space ℳn(S2) and the hypergraph Γnsph encoding projective constraints. In contrast to the original Gnk theory, where codimension-one properties are determined by exactly k particles, the present work considers various cases corresponding to strata of codimension~$1$. These groups admit nice maps to free products of cyclic groups. Among unsolved problems, we emphasize the question how the above construction works for abelian varieties and, in particular, for elliptic curves.
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BibTeX
@misc{manturov2026generalizations,
title = {{Generalizations of the groups $G_n^k$: graphs, moduli spaces, algebraic geometry, spherical braids}},
author = {Vassily Olegovich Manturov},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2608.07976},
eprint = {2608.07976},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.07976},
note = {CC0},
}
RIS
TY - UNPB
TI - Generalizations of the groups G_n^k: graphs, moduli spaces, algebraic geometry, spherical braids
AU - Vassily Olegovich Manturov
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2608.07976
UR - https://arxiv.org/abs/2608.07976
AB - In this work, we construct a generalization of the G_n^k-theory to the case of an arbitrary hypergraph. The case of spherical braids is considered separately, using the stratification of the moduli space ℳ_n(S^2) and the hypergraph Γ_n^sph encoding projective constraints. In contrast to the original G_n^k theory, where codimension-one properties are determined by exactly k particles, the present work considers various cases corresponding to strata of codimension~$1$. These groups admit nice maps to free products of cyclic groups. Among unsolved problems, we emphasize the question how the above construction works for abelian varieties and, in particular, for elliptic curves.
ER -