1,603 research outputs found
Hypercontact structures and Floer homology
We introduce a new Floer theory associated to a pair consisting of a Cartan
hypercontact 3-manifold M and a hyperkaehler manifold X.Comment: 74 page
The three dimensional Fueter equation and divergence free frames
A divergence free frame on a closed three manifold is called regular if every
solution of the linear Fueter equation is constant and is called singular
otherwise. The set of singular divergence free frames is an analogue of the
Maslov cycle. Regular divergence free frames satisfy an analogue of the Arnold
conjecture for flat hyperkaehler target manifolds. The Seiberg-Witten equations
can be viewed as gauged versions of the Fueter equation, and so can the
Donaldson-Thomas equations on certain seven dimensional product manifolds.Comment: Final version, 34 pages. Abhandlungen aus dem Mathematischen Seminar
der Universitaet Hambur
Percolation on uniform infinite planar maps
We construct the uniform infinite planar map (UIPM), obtained as the n \to
\infty local limit of planar maps with n edges, chosen uniformly at random. We
then describe how the UIPM can be sampled using a "peeling" process, in a
similar way as for uniform triangulations. This process allows us to prove that
for bond and site percolation on the UIPM, the percolation thresholds are
p_c^bond=1/2 and p_c^site=2/3 respectively. This method also works for other
classes of random infinite planar maps, and we show in particular that for bond
percolation on the uniform infinite planar quadrangulation, the percolation
threshold is p_c^bond=1/3.Comment: 26 pages, 9 figure
- …