Page 1

Displaying 1 – 10 of 10

Showing per page

The end curve theorem for normal complex surface singularities

Walter D. Neumann, Jonathan Wahl (2010)

Journal of the European Mathematical Society

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 ) ( , 0 ) whose zero set intersects Σ in the knot given by a meridian curve of the exceptional curve corresponding to the given leaf. A “splice quotient singularity” ( X , o ) is described by giving an explicit set of equations describing...

The geometric genus of hypersurface singularities

András Némethi, Baldur Sigurdsson (2016)

Journal of the European Mathematical Society

Using the path lattice cohomology we provide a conceptual topological characterization of the geometric genus for certain complex normal surface singularities with rational homology sphere links, which is uniformly valid for all superisolated and Newton non-degenerate hypersurface singularities.

The Seiberg–Witten invariants of negative definite plumbed 3-manifolds

András Némethi (2011)

Journal of the European Mathematical Society

Assume that Γ is a connected negative definite plumbing graph, and that the associated plumbed 3-manifold M is a rational homology sphere. We provide two new combinatorial formulae for the Seiberg–Witten invariant of M . The first one is the constant term of a ‘multivariable Hilbert polynomial’, it reflects in a conceptual way the structure of the graph Γ , and emphasizes the subtle parallelism between these topological invariants and the analytic invariants of normal surface singularities. The second...

Topological invariants of isolated complete intersection curve singularities

V. H. Jorge Pérez, M. E. Hernandes (2009)

Czechoslovak Mathematical Journal

In this paper we present some formulae for topological invariants of projective complete intersection curves with isolated singularities in terms of the Milnor number, the Euler characteristic and the topological genus. We also present some conditions, involving the Milnor number and the degree of the curve, for the irreducibility of complete intersection curves.

Topology and geometry of caustics in relation with experiments

Alain Joets (1999)

Banach Center Publications

Caustics of geometrical optics are understood as special types of Lagrangian singularities. In the compact case, they have remarkable topological properties, expressed in particular by the Chekanov relation. We show how this relation may be experimentally checked on an example of biperiodic caustics produced by the deflection of the light by a nematic liquid crystal layer. Moreover the physical laws may impose a geometrical constraint, when the system is invariant by some group of symmetries. We...

Currently displaying 1 – 10 of 10

Page 1