Quantum gravity contains incoherent microscopic models with stochastic metric. Decoherence appeared in these models have contributions from stochastic quantum Gravity, which is operating as an effective medium, as well as from conventional uncertainties in the energy of the neutrino (anti-neutrino) beam. All these contributions lead to damping factors modulating the oscillatory terms. In some t...

Given a closed orientable Lagrangian surface L in a closed symplectic four-manifold (X,ω) together with a relative homology class d ∈ H2(X,L;Z) with vanishing boundary in H1(L;Z), we prove that the algebraic number of J-holomorphic discs with boundary on L, homologous to d and passing through the adequate number of points neither depends on the choice of the points nor on the generic choice of ...

This paper proves that the Cancellation Problem has an affirmative answer over a Dedekind containing the rational numbers in dimension three. As a consequence, the Cancellation Problem turns out to have an affirmative answer for a large class of locally nilpotent derivations in dimension four, including the triangular ones.

Seiberg-Witten theory leads to a delicate interplay between Riemannian geometry and smooth topology in dimension four. In particular, the scalar curvature of any metric must satisfy certain non-trivial estimates if the manifold in question has a non-trivial Seiberg-Witten invariant. However, it has recently been discovered [20, 22] that similar statements also apply to other parts of the curvat...