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