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.

In this work, we study a family of Cremona transformations of weighted projective planes which generalize the standard Cremona transformation of the projective plane. Starting from special plane projective curves we construct families of curves in weighted projective planes with special properties. We explain how to co…

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.