13 research outputs found
Symplectic Floer homology of area-preserving surface diffeomorphisms
The symplectic Floer homology HF_*(f) of a symplectomorphism f:S->S encodes
data about the fixed points of f using counts of holomorphic cylinders in R x
M_f, where M_f is the mapping torus of f. We give an algorithm to compute
HF_*(f) for f a surface symplectomorphism in a pseudo-Anosov or reducible
mapping class, completing the computation of Seidel's HF_*(h) for h any
orientation-preserving mapping class.Comment: 57 pages, 4 figures. Revision for publication, with various minor
corrections. Adds results on the module structure and invariance thereo
k-irreducible triangulations of 2-manifolds
This thesis deals with k-irreducible triangulations of closed, compact 2-manifolds without boundary. A triangulation is k-irreducible, if all its closed cycles of length less than k are nullhomotopic and no edge can be contracted without losing this property. k-irreducibility is a generalization of the well-known concept of irreducibility, and can be regarded as a measure of how closely the triangulation approximates a smooth version of the underlying surface.
Research follows three main questions: What are lower and upper bounds for the minimum and maximum size of a k-irreducible triangulation? What are the smallest and biggest explicitly constructible examples? Can one achieve complete classifications for specific 2-manifolds, and fixed k
Collection of abstracts of the 24th European Workshop on Computational Geometry
International audienceThe 24th European Workshop on Computational Geomety (EuroCG'08) was held at INRIA Nancy - Grand Est & LORIA on March 18-20, 2008. The present collection of abstracts contains the 63 scientific contributions as well as three invited talks presented at the workshop
LIPIcs, Volume 258, SoCG 2023, Complete Volume
LIPIcs, Volume 258, SoCG 2023, Complete Volum
Enlarged symmetry algebras of spin chains, loop models, and S-matrices
The symmetry algebras of certain families of quantum spin chains are
considered in detail. The simplest examples possess m states per site (m\geq2),
with nearest-neighbor interactions with U(m) symmetry, under which the sites
transform alternately along the chain in the fundamental m and its conjugate
representation \bar{m}. We find that these spin chains, even with {\em
arbitrary} coefficients of these interactions, have a symmetry algebra A_m much
larger than U(m), which implies that the energy eigenstates fall into sectors
that for open chains (i.e., free boundary conditions) can be labeled by j=0, 1,
>..., L, for the 2L-site chain, such that the degeneracies of all eigenvalues
in the jth sector are generically the same and increase rapidly with j. For
large j, these degeneracies are much larger than those that would be expected
from the U(m) symmetry alone. The enlarged symmetry algebra A_m(2L) consists of
operators that commute in this space of states with the Temperley-Lieb algebra
that is generated by the set of nearest-neighbor interaction terms; A_m(2L) is
not a Yangian. There are similar results for supersymmetric chains with
gl(m+n|n) symmetry of nearest-neighbor interactions, and a richer
representation structure for closed chains (i.e., periodic boundary
conditions). The symmetries also apply to the loop models that can be obtained
from the spin chains in a spacetime or transfer matrix picture. In the loop
language, the symmetries arise because the loops cannot cross. We further
define tensor products of representations (for the open chains) by joining
chains end to end. The fusion rules for decomposing the tensor product of
representations labeled j_1 and j_2 take the same form as the Clebsch-Gordan
series for SU(2). This and other structures turn the symmetry algebra \cA_m
into a ribbon Hopf algebra, and we show that this is ``Morita equivalent'' to
the quantum group U_q(sl_2) for m=q+q^{-1}. The open-chain results are extended
to the cases |m|< 2 for which the algebras are no longer semisimple; these
possess continuum limits that are critical (conformal) field theories, or
massive perturbations thereof. Such models, for open and closed boundary
conditions, arise in connection with disordered fermions, percolation, and
polymers (self-avoiding walks), and certain non-linear sigma models, all in two
dimensions. A product operation is defined in a related way for the
Temperley-Lieb representations also, and the fusion rules for this are related
to those for A_m or U_q(sl_2) representations; this is useful for the continuum
limits also, as we discuss in a companion paper
Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science (STACS'09)
The Symposium on Theoretical Aspects of Computer Science (STACS) is held alternately in France and in Germany. The conference of February 26-28, 2009, held in Freiburg, is the 26th in this series. Previous meetings took place in Paris (1984), Saarbr¨ucken (1985), Orsay (1986), Passau (1987), Bordeaux (1988), Paderborn (1989), Rouen (1990), Hamburg (1991), Cachan (1992), W¨urzburg (1993), Caen (1994), M¨unchen (1995), Grenoble (1996), L¨ubeck (1997), Paris (1998), Trier (1999), Lille (2000), Dresden (2001), Antibes (2002), Berlin (2003), Montpellier (2004), Stuttgart (2005), Marseille (2006), Aachen (2007), and Bordeaux (2008). ..