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Construction and Properties of the t-Invariant

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Abstract

Special spine theory is used for constructing a new invariant of compact 3-manifolds: the t-invariant. The behavior of the invariant under (boundary) connected sum is investigated. One of the Turaev―Viro invariants is expressed via the t-invariant. The t-invariant is interpreted from the point of view of TQFT. The values of the t-invariant are computed for lens spaces and for all closed oriented 3-manifolds of complexity at most six. It is proved that the set of values of the t-invariant on Seifert manifolds with fixed base (which is a closed surface) and fixed number of singular fibers is finite. Bibliography: 10 titles.

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Authors and Affiliations

  1. Chelyabinsk State University, Russia

    S. V. Matveev, M. A. Ovchinnikov & M. V. Sokolov

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  1. S. V. Matveev
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  2. M. A. Ovchinnikov
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  3. M. V. Sokolov
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Matveev, S.V., Ovchinnikov, M.A. & Sokolov, M.V. Construction and Properties of the t-Invariant. Journal of Mathematical Sciences 113, 849–855 (2003). https://doi.org/10.1023/A:1021247621259

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