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Representations of the Kauffman skein algebra II: punctured surfaces
Representations of the Kauffman skein algebra II punctured surfaces Geometric Topology
2012/6/29
In earlier work, we constructed invariants of irreducible representations of the Kauffman skein algebra of a surface. We introduce here an inverse construction, which to a set of possible invariants a...
The minimal genus problem for elliptic surfaces
4-manifold elliptic surface diffeomorphism group minimal genus
2012/6/25
We partly solve the minimal genus problem for embedded surfaces in the case of elliptic 4-manifolds. This involves a certain restricted transitivity property of the action of the orientation preservin...
Skein algebras and cluster algebras of marked surfaces
Skein algebras cluster algebras marked surfaces Quantum Algebra Geometric Topology
2012/4/17
This paper defines several algebras associated to an oriented surface S with a finite set of marked points on the boundary. The first is the skein algebra Sk_q(S), which is spanned by links in the sur...
On visualization of the linearity problem for mapping class groups of surfaces
visualization linearity problem mapping class groups surfaces
2012/3/1
We derive two types of linearity conditions for mapping class groups of orientable surfaces; one for once-punctured surface, and the other for closed surface, respectively. For the once-punctured case...
Computing the crosscap number of a knot using integer programming and normal surfaces
integer programming normal surfaces crosscap number of a knot Geometric Topology
2011/9/5
Abstract: The crosscap number of a knot is an invariant describing the non-orientable surface of smallest genus that the knot bounds. Unlike knot genus (its orientable counterpart), crosscap numbers a...