非交换Reidemeister挠率与Morse-Novikov理论
几何拓扑
2010-07-08 v5
摘要
给定一个闭定向流形的圆值Morse函数，我们证明在非交换形式Laurent多项式环上的Reidemeister挠率等于该环上某个非交换Lefschetz型zeta函数与Novikov复形代数挠率的乘积。本文将Hutchings和Lee关于交换系数的结果推广到斜域情形。作为推论，我们得到了高阶Reidemeister挠率的Morse理论与动力系统描述。
引用
@article{arxiv.0906.4174,
title = {Non-commutative Reidemeister torsion and Morse-Novikov theory},
author = {Takahiro Kitayama},
journal= {arXiv preprint arXiv:0906.4174},
year = {2010}
}
备注
12 pages; 13 pages, added important references for the introduction; changed the fixed generator $t$ into the inverse one; 15 pages, redefined the non-commutative zeta function; to appear in Proceedings of the American Mathematical Society