ON YETTER S INVARIANT AND AN EXTENSION OF THEDIJKGRAAF-WITTEN INVARIANT TO CATEGORICAL GROUPS


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    • Abstract:  JO ~AO FARIA MARTINS AND TIMOTHY PORTER Abstract. We give an interpretation of Yetter's Invariant of manifolds M in terms ofthe homotopy type of the function space TOP( M, B(G)), where G is a crossed moduleand B(G) is its classifying space. From this formulation, there follows that Yetter'sinvariant depends only on the homotopy type of M, and the weak homotopy type of thecrossed 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 classifyingspaces, 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 straightforwardexten sion to crossed complexes is also considered.

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