稳定辛范畴与 Kontsevich 猜想
代数拓扑
2015-11-03 v3 数学物理
K理论与同调
math.MP
辛几何
摘要
我们考虑 \cite{N} 中定义的稳定辛范畴的一个定向版本。我们证明该范畴中固定每个对象的幺半自同构群包含一个自然子群，同构于 Grothendieck--Teichmüller 群的可解商（或分次阿贝尔商）。这建立了 Kontsevich 猜想的一个稳定版本，该猜想指出与 Grothendieck--Teichmüller 群密切相关的群作用于某些场论的模空间上 \cite{KO}。我们还证明，Grothendieck--Teichmüller 群的上述商也是稳定辛范畴上的典范表示（或纤维函子）的 motive 幺半自同构群。
引用
@article{arxiv.1212.6905,
title = {The Stable Symplectic category and a conjecture of Kontsevich},
author = {Nitu Kitchloo and Jack Morava},
journal= {arXiv preprint arXiv:1212.6905},
year = {2015}
}
备注
The paper has been largely reorganized to interpret the action of the Grothendieck--Teichm\"uller group in the context of a conjecture of Kontsevich. The title has been changed accordingly. The section on the Waldhausen K-theory of $s\Omega$ has been removed and will form part of a separate document. All other sections have been preserved