State-Sum Invariants of 4-Manifolds I

Details State-Sum Invariants of 4-Manifolds I State-Sum Invariants of 4-Manifolds I

1994-09-27

arxiv.org/abs/hep-th/9409167v1

Physics

High Energy Physics

High Energy Physics - Theory

46 pages

Scientific paper

We provide, with proofs, a complete description of the authors' construction of state-sum invariants announced in [CY], and its generalization to an arbitrary (artinian) semisimple tortile category. We also discuss the relationship of these invariants to generalizations of Broda's surgery invariants [Br1,Br2] using techniques developed in the case of the semi-simple sub-quotient of $Rep(U_q(sl_2))$ ($q$ a principal $4r^{th}$ root of unity) by Roberts [Ro1]. We briefly discuss the generalizations to invariants of 4-manifolds equipped with 2-dimensional (co)homology classes introduced by Yetter [Y6] and Roberts [Ro2], which are the subject of the sequel. (citations refer to bibliography in the paper)

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