On $3$-dimensional foliated dynamical systems and Hilbert type reciprocity law
Dynamical Systems
2021-06-08 v1 Geometric Topology
Number Theory
Abstract
We show some fundamental results concerning -dimensional foliated dynamical systems (FDS for short) introduced by Deninger. Firstly, we give a decomposition theorem for an FDS, which yields a classification of FDS's. Secondly, for each type of the classification, we construct concrete examples of FDS's. Finally, by using the integration theory for smooth Deligne cohomology, we introduce geometric analogues of local symbols and show a Hilbert type reciprocity law for an FDS. Our results answer the question posed by Deninger.
Cite
@article{arxiv.1906.02424,
title = {On $3$-dimensional foliated dynamical systems and Hilbert type reciprocity law},
author = {Junhyeong Kim and Masanori Morishita and Takeo Noda and Yuji Terashima},
journal= {arXiv preprint arXiv:1906.02424},
year = {2021}
}
Comments
30 pages, 3 figures