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In this paper, we shall be concerned with a relation between TQFTs and cutand paste invariants introduced by Karras, Kreck, Neumann and Ossa. Cut andpaste invariants, or SK invariants, are functions on the set of smoothmanifolds that are invariant under the cutting and pasting operation. Centralto the work in this paper are also SKK invariants, whose values on cut andpaste equivalent manifolds differ by an error term depending only on theglueing diffeomorphism. Here we investigate a surprisingly natural grouphomomorphism between the group of invertible TQFTs and the group of SKKinvariants and describe how these groups fit into an exact sequence. Weconclude in particular that all positive real-valued SKK invariants can berealized as restrictions of invertible TQFTs. All manifolds are smooth andoriented throughout unless stated otherwise.

Relating Cut and Paste Invariants and TQFTs