math

I did my PhD in Topology although I originally I wanted to work in Mathematical Logic. My PhD thesis was on disjoint topological embeddings of 2-spheres in simply connected 4-manifolds, I basically wrote a theorem which gives a necessary and sufficient condition for disjointly embedding two 2-spheres in a simply connected four manifolds.

This was a couple of years after Donaldson’s groundbreaking work and a couple of years before Witten’s breakthroughs. Subsequently while at the Max-Planck Institute for Mathematis in Bonn, Germany I got interested in classical knot theory. Solved a 20 year old open problem, I wrote some papers on unknotting moves, one on Knot Adjacency with Effstratia Kalfagianni and one I like the most on Vassiliev invariants which I never cared to publish. It can be found at arxiv.org. My knot theory papers can be mostly located on Google Scholar.

My entry in the Mathematics Genealogy Project. My Erdos number apppears to be 5. It goes over Effie Kalfagianni, Xiao-Song Lin, Michael Friedman and Laszlo Lovasz.

A list of my math papers:

Askitas, Nikos ;  Kalfagianni, Efstratia . On knot adjacency.
Topology Appl.  126  (2002),  no. 1-2, 63–81.

Askitas, Nikos . Grids as unknotting operations. Knots in Hellas ’98
(Delphi), 18–26, Ser. Knots Everything, 24, World Sci. Publ.,
River Edge, NJ,  2000.

Askitas, N. A.  A grid of type pxq with gcd{p,q}=6 unknots.
J. Knot Theory Ramifications  9  (2000),  no. 3, 285–292.

Askitas, Nikolaos A.  On 4-equivalent tangles.
Kobe J. Math.  16  (1999),  no. 1, 87–91.

Askitas, N. λ-unknotting-number-one knots need not be prime.
J. Knot Theory Ramifications  8  (1999),  no. 7, 831–834.

Askitas, Nikolaos A.  A note on 4-equivalence.
J. Knot Theory Ramifications  8  (1999),  no. 3, 261–263.

Askitas, N.  Multi-# unknotting operations: a new family of local moves on a
knot diagram and related invariants of knots.
J. Knot Theory Ramifications  7  (1998),  no. 7, 857–871.

Askitas, N.  A note on the #-unknotting operation.
J. Knot Theory Ramifications  7  (1998),  no. 6, 713–718.

Askitas, Nikolaos . On pairs of locally flat 2-spheres in simply
connected 4-manifolds. Math. Z.  228  (1998),  no. 1, 131–153.

Askitas, Nikolaos . Erratum: “Embeddings of 2-spheres in 4-manifolds”
[Manuscripta Math. 89 (1996), no. 1, 35–47]. Manuscripta Math.  90
(1996),  no. 1, 137–138

Askitas, Nikolaos . Embeddings of 2-spheres in 4-manifolds.
Manuscripta Math.  89  (1996),  no. 1, 35–47.