Introduces relative eta invariants for Dirac operators coinciding at infinity on non-compact manifolds with bounded curvature, yielding a spectral flow formula, a new proof of a Gromov-Lawson result, and an APS index theorem generalization to non-compact boundaries.
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The moduli space of mean convex two-spheres in complete orientable 3-manifolds with nonnegative Ricci curvature is path-connected; mean convex Heegaard tori have one or two path components depending on a precise characterisation.
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Relative eta invariant and uniformly positive scalar curvature on non-compact manifolds
Introduces relative eta invariants for Dirac operators coinciding at infinity on non-compact manifolds with bounded curvature, yielding a spectral flow formula, a new proof of a Gromov-Lawson result, and an APS index theorem generalization to non-compact boundaries.
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Mean Curvature Flow and Heegaard Surfaces in Lens Spaces
The moduli space of mean convex two-spheres in complete orientable 3-manifolds with nonnegative Ricci curvature is path-connected; mean convex Heegaard tori have one or two path components depending on a precise characterisation.