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Paper accepted in Transactions of the American Mathematical Society

Jørgen E. Andersen and William E. Mistegård gets a paper accepted in Transactions of the American Mathematical Society.

2019.01.15 | Christine Dilling

The paper Asymptotic expansions of the Witten-Reshetikhin-Turaev invariants of mapping tori I by Andersen and Mistegård was recently accepted in Transactions of the American Mathematical Society published by the American Mathematical Society

In this paper the authors engage in a general study of the asymptotic expansion of the Witten-Reshetikhin-Turaev invariants of mapping tori of surface mapping class group elements. They use the geometric construction of the Witten-Reshetikhin-Turaev TQFT via the geometric quantization of moduli spaces of flat connections on surfaces. They identify assumptions on the mapping class group elements that allow them to provide a full asymptotic expansion. The proof of this relies on their new results regarding asymptotic expansions of oscillatory integrals, which allows them to go significantly beyond the standard transversely cut out assumption on the fixed point set. Their results apply to mapping classes of a punctured surface of genus at least one. In particular, they show that their results apply to all pseudo-Anasov mapping classes on a punctured torus and show by example that their assumptions on the mapping class group elements are strictly weaker than hithero successfully considered assumptions in this context. 

Link to arXiv

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