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Relating Cut and Paste Invariants and Tqfts
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Abstract
In this paper, we are concerned with a relation between TQFTs and the cut and paste SKK invariants introduced by Karras, Kreck, Neumann, and Ossa. Cut and paste SKK invariants are functions on the set of smooth manifolds whose values on cut and paste equivalent manifolds differ by an error term depending only on the glueing diffeomorphisms. Here we investigate a surprisingly natural group homomorphism between the group of invertible TQFTs and the group of SKK invariants and describe how these groups fit into an exact sequence. We conclude in particular that all positive real-valued SKK invariants can be realized as restrictions of invertible TQFTs.
Oxford University Press (OUP)
Title: Relating Cut and Paste Invariants and Tqfts
Description:
Abstract
In this paper, we are concerned with a relation between TQFTs and the cut and paste SKK invariants introduced by Karras, Kreck, Neumann, and Ossa.
Cut and paste SKK invariants are functions on the set of smooth manifolds whose values on cut and paste equivalent manifolds differ by an error term depending only on the glueing diffeomorphisms.
Here we investigate a surprisingly natural group homomorphism between the group of invertible TQFTs and the group of SKK invariants and describe how these groups fit into an exact sequence.
We conclude in particular that all positive real-valued SKK invariants can be realized as restrictions of invertible TQFTs.
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