Lie algebroids and Poisson-Nijenhuis structures

For any Riemannian foliation F on a closed manifold M with an arbitrary bundle-like metric, leafwise heat flow of differential forms is proved to preserve smoothness on M at infinite time. This result and its proof have consequences about the space of bundle-like metrics on M, about the dimension of the space of leafwise harmonic forms, and mainly about the second term of the differentiable spectral sequence of F.

dg-ga↗

arXiv2018

A Simple Geometric Representative for $μ$ of a Point

For $SU(2)$ (or $SO(3)$) Donaldson theory on a 4-manifold $X$, we construct a simple geometric representative for $μ$ of a point. Let $p$ be a generic point in $X$. Then the set $\{ [A] | F_A^-(p) $ is reducible $\}$, with coefficient -1/4 and appropriate orientation, is our desired geometric representative.

dg-ga↗

arXiv2013

Moduli spaces of PU(2)-monopoles

The goal of this article was the S^1-equivariant transversality-problem and the compactification-problem for the moduli spaces of (perturbed) PU(2)-monopoles. A substantially improved version entitled "Moduli spaces of PU(2)-monopoles (revised version)" which gives simpler, clearer proofs of the transversality results, has been published on arxiv in June 99 and appeared in Asian J. Math, see Moduli spaces of PU(2)-Monopoles, Asian J. Math. Vol. 4, No. 2 (2000), 391-436.

dg-ga↗