On Yetter's Invariant and an Extension of the Dijkgraaf-Witten Invariant to Categorical Groups

Details On Yetter's Invariant and an Extension of the Dijkgraaf-Witten Invariant to Categorical Groups On Yetter's Invariant and an Extension of the Dijkgraaf-Witten Invariant to Categorical Groups

2006-08-19

arxiv.org/abs/math/0608484v2

Theor.Appl.Categor.18:118-150,2007

Mathematics

Quantum Algebra

45 pages. Several improvements

Scientific paper

We give an interpretation of Yetter's Invariant of manifolds $M$ in terms of the homotopy type of the function space $TOP(M,B(G))$, where $G$ is a crossed module and $B(G)$ is its classifying space. From this formulation, there follows that Yetter's invariant depends only on the homotopy type of $M$, and the weak homotopy type of the crossed module $G$. We use this interpretation to define a twisting of Yetter's Invariant by cohomology classes of crossed modules, defined as cohomology classes of their classifying spaces, in the form of a state sum invariant. In particular, we obtain an extension of the Dijkgraaf-Witten Invariant of manifolds to categorical groups. The straightforward extension to crossed complexes is also considered.

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