We count how many ‘different’ Morse functions exist on the 2-sphere. There are several ways of declaring that two Morse functions f and g are ‘indistinguishable’ but we concentrate only on two… (More)

The eta invariant was introduced in mathematics in the celebrated papers [APS13] as a correction term in an index formula for a non-local, elliptic boundary value problem and since then it has been… (More)

Given a compact, connected Riemann manifold without boundary (M, g) of dimensionm and a large positive constantLwe denote byUL the subspace ofC∞(M) spanned by eigenfunctions of the Laplacian… (More)

We verify the conjecture formulated in [31] for suspension singularities of type g(x, y, z) = f(x, y) + z, where f is an irreducible plane curve singularity. More precisely, we prove that the… (More)

We construct some natural metric connections on metric contact manifolds compatible with the contact structure and characterized by the Dirac operators they determine. In the case of CR manifolds… (More)

We compute virtual dimensions of finite energy Seiberg-Witten moduli spaces on 4-manifolds bounding Seifert fibrations. The key moment is the determination of certain eta invariants. As an… (More)

The “old” instanton theory naturally lead to the instanton Floer homology of a 3-manifold N as the missing piece in a general gluing formula for the Donaldson invariants. Similarly, the… (More)

We verify the conjecture formulated in [18] for any normal surface singularity which admits a good C∗-action. The main result connects the Seiberg-Witten invariant of the link (associated with a… (More)