arXiv research

Kervaire's sphere-link is equivalent to a ribbon sphere-link, simplifying complex 2-complexes.

Author provides an alternate proof of the free ribbon lemma.

It has long been known that every quasi-homogeneous normal complex surface singularity with Q-homology sphere link has universal abelian cover a Brieskorn complete intersection singularity. We describe a broad generalization: First, one has a class of complete intersection normal complex surface singularities called "s…

Paper confirms Whitehead's conjecture for aspherical 2-complexes.

Free surface-links are shown to be ribbon links.

While the topological types of {normal} surface singularities with homology sphere link have been classified, forming a rich class, until recently little was known about the possible analytic structures. We proved in [Geom. Topol. 9(2005) 699-755] that many of them can be realized as complete intersection singularities…

This note proves properties of surface-links with trivial components.

Study Cremona transformations in weighted projective planes to find rational cuspidal curves and Zariski pairs.

Study topological Iwasawa invariants for 3-sphere links, proving density results.

Flat semigroups can represent normal weighted homogeneous surface singularities.

Proves representability of complex semigroup systems.

For the link $M$ of a normal complex surface singularity $(X,0)$ we ask when a knot $K\subset M$ exists for which the answer to whether $K$ is the link of the zero set of some analytic germ $(X,0)\to (\mathbb C,0)$ affects the analytic structure on $(X,0)$. We show that if $M$ is an integral homology sphere then such a…

New invariant for links in 3-sphere computed and computed using diagrams.

Study involutions on 3D small covers, proving quotient spaces are linked 2-spheres.

We prove the "End Curve Theorem," which states that a normal surface singularity $(X,o)$ with rational homology sphere link $Σ$ is a splice-quotient singularity if and only if it has an end curve function for each leaf of a good resolution tree. An "end-curve function" is an analytic function $(X,o)\to (\C,0)$ whose ze…

Perelman's proof confirmed, new method uses 4D topology.

Analytic lattice cohomology defined for isolated singularities, linking to Heegaard Floer cohomology.

Let $(X,o)$ be a complex normal surface singularity with rational homology sphere link and let $\widetilde{X}$ be one of its good resolutions. Fix an effective cycle $Z$ supported on the exceptional curve and also a possible Chern class $l'\in H^2(\widetilde{X},\mathbb{Z})$. Define ${\rm Eca}^{l'}(Z)$ as the space of e…

Study on knots and dynamics on three-sphere, linking bounds, and upper action bounds.