Homotopy field theory in dimension 3 and crossed group-categories
Homotopy field theory in dimension 3 and crossed group-categories
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发表时间：
2000-05
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通讯作者：
V. Turaev
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作者：
V. Turaev
三维同伦量子场论（HQFT）可以描述为具有给定空间中映射的同伦类的曲面和3-协点的TQFT。对于群$\pi$，我们引入了模交叉$\pi$-范畴的概念，并证明了这样的范畴产生了目标空间$K(\pi,1)$的三维HQFT。这包括三维$\pi$流形的数值不变量和二维同伦模函子。我们还引入并讨论了拟三角形交叉Hopf $\pi$-协代数的平行概念。
A 3-dimensional homotopy quantum field theory (HQFT) can be described as a TQFT for surfaces and 3-cobordisms endowed with homotopy classes of maps into a given space. For a group $\pi$, we introduce a notion of a modular crossed $\pi$-category and show that such a category gives rise to a 3-dimensional HQFT with target space $K(\pi,1)$. This includes numerical invariants of 3-dimensional $\pi$-manifolds and a 2-dimensional homotopy modular functor. We also introduce and discuss a parallel notion of a quasitriangular crossed Hopf $\pi$-coalgebra.