We prove that any Fano manifold of coindex three admitting nef tangent bundle is homogeneous.
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The paper studies Einstein metrics on specific manifolds and their rigidity properties.
problem Investigating rigidity of Einstein metrics on homogeneous Gray manifolds.
method Computing coindex and analyzing infinitesimal deformations of Einstein metrics.
result Infinitesimal Einstein deformations on are not integrable.
The paper defines a new invariant for links and uses it to show non-sliceness.
problem Determining whether a link is slice or not.
method Defining a new concordance invariant from the Seifert form and using it to bound the slice Euler characteristic.
result The Witt coindex provides an upper bound for the slice Euler characteristic of a link.
The purpose of this paper is to study finite dimensional equivariant moduli problems from the viewpoint of stratification theory. We show that there exists a stratified obstruction system for a finite dimensional equivariant moduli problem. In addition, we define a coindex for a G-vector bundle which is determined by t…
Coupled embeddabilitymath.GT
Defines coupled embeddability for maps on products of spaces, generating examples and nonexamples.
problem Understanding when maps on products of spaces can be embedded.
method Uses known results for nonsingular biskew and bilinear maps, studies genericity properties, extends Whitney embedding theorems, and relates to -coindex of embedding spaces.
result Generates strong obstructions to coupled embeddability in terms of combinatorics of triangulations.
The paper studies stability of Einstein metrics on non-simple Lie group homogeneous spaces.
problem Classifying compact homogeneous spaces with standard Einstein metrics.
method Analysis of scalar curvature functional and coindex.
result Most standard Einstein metrics on non-simple Lie group homogeneous spaces are unstable.
We study the linear stability of Einstein metrics of Riemannian submersion type. First, we derive a general instability condition for such Einstein metrics and provide some applications. Then we study instability arising from Riemannian product structures on the base. As an application, we estimate the coindex of the E…
New Einstein metrics identified on a specific full flag manifold.
problem Investigating Einstein metrics on a full flag manifold.
method Analyzing -stability of Einstein metrics on .
result Identified four new Einstein metrics on , confirming pairwise non-homotheticity.
Study on stability of non-diagonal Einstein metrics on specific homogeneous spaces.
problem Stability analysis of non-diagonal Einstein metrics on .
method Formula for scalar curvature, study of stability with Hilbert action.
result Non-diagonal Einstein metrics on are unstable with different coindexes.
Counterexample disproves Borde-Sorkin conjecture on causal continuity of Morse spacetimes.
problem Disproving the Borde-Sorkin conjecture on causal continuity of Morse spacetimes.
method Provided a counterexample with low regularity causal structure and causal bubbling.
result Borde-Sorkin conjecture does not hold for Morse spacetimes with large anisotropy.
We prove a semi-Riemannian version of the celebrated Morse Index Theorem for geodesics in semi-Riemannian manifolds; we consider the general case of both endpoints variable on two submanifolds. The key role of the theory is played by the notion of the {\em Maslov index} of a semi-Riemannian geodesic, which is a homolog…