论文标题
棕色函子诱导的TQFT的一对同质理论版本
A pair of homotopy-theoretic version of TQFT's induced by a Brown functor
论文作者
论文摘要
本文的目的是研究通过构造构造TQFT（简称射击HTQFT）构造的一些障碍类别。对称的单射射灯函子给出了一个投影HTQFT，其域是尖的有限CW空间的Cospan类别，而不是COBORDISM类别。我们从$ \ mathsf {hopf}^\ mathsf {bc} _k $ - valuew brown fuctor构造一对投影htqft的htqft，其中$ \ m artsf {hopf}^\ mathsf {hopf}^\ mathsf {bc} _k $是bicmumnative $ hopf alggebras and field partial and partials and partials的类别。棕色函子的路径综合。他们通过与投影表达相关的第二个同种学类别的类似物诱导障碍物类别。在本文中，我们得出了这些障碍类别的一些公式。我们应用该公式来证明降低了共同体和统计途径综合的尺寸，将其提升为HTQFT的尺寸。在另一个应用程序中，我们从普通的$ \ Mathsf {hopf}^\ Mathsf {bc} _k $ valued同源理论中复制Dijkgraaf-Witten TQFT和Turaev-Viro tqft。
The purpose of this paper is to study some obstruction classes induced by a construction of a homotopy-theoretic version of projective TQFT (projective HTQFT for short). A projective HTQFT is given by a symmetric monoidal projective functor whose domain is the cospan category of pointed finite CW-spaces instead of a cobordism category. We construct a pair of projective HTQFT's starting from a $\mathsf{Hopf}^\mathsf{bc}_k$-valued Brown functor where $\mathsf{Hopf}^\mathsf{bc}_k$ is the category of bicommutative Hopf algebras over a field $k$ : the cospanical path-integral and the spanical path-integral of the Brown functor. They induce obstruction classes by an analogue of the second cohomology class associated with projective representations. In this paper, we derive some formulae of those obstruction classes. We apply the formulae to prove that the dimension reduction of the cospanical and spanical path-integrals are lifted to HTQFT's. In another application, we reproduce the Dijkgraaf-Witten TQFT and the Turaev-Viro TQFT from an ordinary $\mathsf{Hopf}^\mathsf{bc}_k$-valued homology theory.
