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    Gromov-Lawson concordance implies isotopy for positive intermediate scalar curvature


    McEvoy, Luke (2025) Gromov-Lawson concordance implies isotopy for positive intermediate scalar curvature. PhD thesis, National University of Ireland Maynooth.

    Abstract

    This thesis generalises a result of M. Walsh by proving that Gromov–Lawson concordance implies isotopy in the space of Riemannian metrics with positive (p, n)-intermediate scalar curvature. We work in the setting of closed, simply-connected manifolds of dimension n → 5, equipped with Morse functions that satisfy suitable admissibility and cancellation conditions. Building on the surgery stability results of Gromov-Lawson and Labbi, we construct a relative isotopy between specific metrics and use it to prove that any Gromov–Lawson (sp,n > 0)- concordant metrics are isotopic through positive (p, n)-intermediate scalar curvature metrics. The main result shows that for a closed, simply-connected manifold M of dimension at least 5, Gromov–Lawson concordance implies isotopy in Rsp,n>0(M), thereby extending the known relationship between isotopy and concordance from the scalar curvature case to the intermediate curvature setting.
    Item Type: Thesis (PhD)
    Keywords: Gromov-Lawson concordance; isotopy; positive intermediate scalar curvature;
    Academic Unit: Faculty of Science and Engineering > Mathematics and Statistics
    Item ID: 21230
    Depositing User: IR eTheses
    Date Deposited: 24 Feb 2026 12:14
    Use Licence: This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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