Finite groups, spherical 2-categories, and 4-manifold invariants. arXiv:math.QA/9903003
| Citations: | 12 - 5 self |
BibTeX
@MISC{Mackaay_finitegroups,,
author = {Marco Mackaay and Área Departamental De Matemática},
title = {Finite groups, spherical 2-categories, and 4-manifold invariants. arXiv:math.QA/9903003},
year = {}
}
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Abstract
In this paper we define a class of state-sum invariants of compact closed oriented piece-wise linear 4-manifolds using finite groups. The definition of these state-sums follows from the general abstract construction of 4-manifold invariants using spherical 2-categories, as we defined in [32], although it requires a slight generalization of that construction. We show that the state-sum invariants of Birmingham and Rakowski [11, 12, 13], who studied Dijkgraaf-Witten type invariants in dimension 4, are special examples of the general construction that we present in this paper. They showed that their invariants are nontrivial by some explicit computations, so our construction includes interesting examples already. Finally, we indicate how our construction is related to homotopy 3-types. This connection suggests that there are many more interesting examples of our construction to be found in the work on homotopy 3-types, such as [15], for example. 1 1
