Finite Groups, Spherical 2-Categories, and 4-Manifold Invariants

✍ Scribed by Marco Mackaay

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 339 KB
• Volume: 153
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1006/aima.1999.1909

✦ Synopsis

In this paper we define a class of state-sum invariants of closed oriented piecewise 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 an earlier paper. We show that the statesum invariants of Birmingham and Rakowski, 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 non-trivial 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, by Brown, for example.

2000

Academic Press the authors show that any finite dimensional semi-simple associative algebra, A, can be used for the construction of state-sum invariants of 2-manifolds (surfaces). This is not the place to recall the construction in