标题： 受限的(2+1)-拓扑量子场论支持加厚和实心环面 显示英文标题

标题： Restricted (2+1)-TQFTs supported by thickened and solid tori

摘要： 一个忠实的$(1+1)$拓扑量子场论（TQFT）最近已被构建出来，但忠实的$(2+1)$拓扑量子场论的存在性仍然是一个未解的问题，这个问题涵盖了曲面映射类群线性化这一困难问题。 为绕过这一难题，我们构造了三维Cobordism范畴的一个子范畴，该子范畴包含了不相交的环面并以及它们之间最简单的Cobordism。 在此基础上，我们定义了拓扑量子场论，这些理论能够区分先前由量子不变量显示无法区分的一对环面丛和透镜空间。 显示英文摘要

摘要： A faithful $(1+1)$ TQFT has recently been constructed, but the existence of a faithful $(2+1)$ TQFT remains an open question, that subsumes the hard problem of linearity of mapping class groups of surfaces. To circumvent the latter problem we construct a subcategory of the category of 3-cobordisms, containing disjoint unions of tori and simplest cobordisms between them. On this we define TQFTs that are able to distinguish pairs of torus bundles and lens spaces, previously shown not to be distinguishable by quantum invariants.