与三维流形 LMO 不变量相关的拓扑量子场论
几何拓扑
2008-11-26 v2 量子代数
摘要
我们构造了一个（在 Atiyah 意义下的）拓扑量子场论（Topological Quantum Field Theory, TQFT），它与三维流形的通用有限型不变量相关，作为一个从具有参数化边界的三维流形范畴（满足某些附加条件）到代数-组合范畴的函子。它与其关于自然分次截断一并构建，并且我们证明这些 TQFT 是非退化的且无反常。该 TQFT（们）诱导出映射类群中包含一个 Torelli 群的子群 的（一系列）表示。N=1 截断给出了 Casson-Walker-Lescop 不变量的一个 TQFT。
引用
@article{arxiv.math/0508220,
title = {A TQFT associated to the LMO invariant of three-dimensional manifolds},
author = {Dorin Cheptea and Thang T Q Le},
journal= {arXiv preprint arXiv:math/0508220},
year = {2008}
}
备注
28 pages, 13 postscript figures. Version 2 (Section 1 has been considerably shorten, and section 3 has been slightly shorten, since they will constitute a separate paper. Section 4, which contained only announce of results, has been suprimated; it will appear in detail elsewhere. Consequently some statements have been re-numbered. No mathematical changes have been made.)