Narrow Results

In this paper, we prove that for any closed, connected, oriented $3$-manifold $M$, there exists an infinite family of 2-fold branched covers of $M$ that are hyperbolic 3-manifolds and surface bundles over the circle with arbitrarily large volume.

Kodaira fibrations are surfaces of general type with a non-isotrivial fibration, which are differentiable fiber bundles. They are known to have positive signature divisible by $4$. Examples are known only with signature 16 and more. We review approaches to construct examples of low signature which admit two independent fibrations. Special attention is paid to ramified covers of product of curves which we analyze by studying the monodromy action for bundles of punctured curves. As a by-product, we obtain a classification of all fix-point-free automorphisms on curves of genus at most $9$.

Critical surfaces can be regarded as topological index 2 minimal surfaces which was introduced by David Bachman. In this paper, we give a sufficient condition and a necessary condition for self-amalgamated Heegaard surfaces to be critical.

In this paper, we show that every closed orientable surface bundle over the circle is represented by a fibered link in the 3-sphere with framings induced by the fibration of the complement.