821 research outputs found
Remarks on the classification of quasitoric manifolds up to equivariant homeomorphism
We give three sufficient criteria for two quasitoric manifolds (M,M') to be
(weakly) equivariantly homeomorphic.
We apply these criteria to count the weakly equivariant homeomorphism types
of quasitoric manifolds with a given cohomology ring.Comment: 11 page
Symplectic geometry on moduli spaces of J-holomorphic curves
Let (M,\omega) be a symplectic manifold, and Sigma a compact Riemann surface.
We define a 2-form on the space of immersed symplectic surfaces in M, and show
that the form is closed and non-degenerate, up to reparametrizations. Then we
give conditions on a compatible almost complex structure J on (M,\omega) that
ensure that the restriction of the form to the moduli space of simple immersed
J-holomorphic Sigma-curves in a homology class A in H_2(M,\Z) is a symplectic
form, and show applications and examples. In particular, we deduce sufficient
conditions for the existence of J-holomorphic Sigma-curves in a given homology
class for a generic J.Comment: 16 page
Bubble divergences from cellular cohomology
We consider a class of lattice topological field theories, among which are
the weak-coupling limit of 2d Yang-Mills theory, the Ponzano-Regge model of 3d
quantum gravity and discrete BF theory, whose dynamical variables are flat
discrete connections with compact structure group on a cell 2-complex. In these
models, it is known that the path integral measure is ill-defined in general,
because of a phenomenon called `bubble divergences'. A common expectation is
that the degree of these divergences is given by the number of `bubbles' of the
2-complex. In this note, we show that this expectation, although not realistic
in general, is met in some special cases: when the 2-complex is simply
connected, or when the structure group is Abelian -- in both cases, the
divergence degree is given by the second Betti number of the 2-complex.Comment: 5 page
A categorification of Morelli's theorem
We prove a theorem relating torus-equivariant coherent sheaves on toric
varieties to polyhedrally-constructible sheaves on a vector space. At the level
of K-theory, the theorem recovers Morelli's description of the K-theory of a
smooth projective toric variety. Specifically, let be a proper toric
variety of dimension and let M_\bR = \mathrm{Lie}(T_\bR^\vee)\cong \bR^n
be the Lie algebra of the compact dual (real) torus T_\bR^\vee\cong U(1)^n.
Then there is a corresponding conical Lagrangian \Lambda \subset T^*M_\bR and
an equivalence of triangulated dg categories \Perf_T(X) \cong
\Sh_{cc}(M_\bR;\Lambda), where \Perf_T(X) is the triangulated dg category of
perfect complexes of torus-equivariant coherent sheaves on and
\Sh_{cc}(M_\bR;\Lambda) is the triangulated dg category of complex of sheaves
on M_\bR with compactly supported, constructible cohomology whose singular
support lies in . This equivalence is monoidal---it intertwines the
tensor product of coherent sheaves on with the convolution product of
constructible sheaves on M_\bR.Comment: 20 pages. This is a strengthened version of the first half of
arXiv:0811.1228v3, with new results; the second half becomes
arXiv:0811.1228v
Semitoric integrable systems on symplectic 4-manifolds
Let M be a symplectic 4-manifold. A semitoric integrable system on M is a
pair of real-valued smooth functions J, H on M for which J generates a
Hamiltonian S^1-action and the Poisson brackets {J,H} vanish. We shall
introduce new global symplectic invariants for these systems; some of these
invariants encode topological or geometric aspects, while others encode
analytical information about the singularities and how they stand with respect
to the system. Our goal is to prove that a semitoric system is completely
determined by the invariants we introduce
Moduli spaces of toric manifolds
We construct a distance on the moduli space of symplectic toric manifolds of
dimension four. Then we study some basic topological properties of this space,
in particular, path-connectedness, compactness, and completeness. The
construction of the distance is related to the Duistermaat-Heckman measure and
the Hausdorff metric. While the moduli space, its topology and metric, may be
constructed in any dimension, the tools we use in the proofs are
four-dimensional, and hence so is our main result.Comment: To appear in Geometriae Dedicata, minor changes to previous version,
19 pages, 6 figure
Witten's 2+1 gravity on R x (Klein bottle)
Witten's formulation of 2+1 gravity is investigated on the nonorientable
three-manifold R x (Klein bottle). The gauge group is taken to consist of all
four components of the 2+1 Poincare group. We analyze in detail several
components of the classical solution space, and we show that from four of the
components one can recover nondegenerate spacetime metrics. In particular, from
one component we recover metrics for which the Klein bottles are spacelike. An
action principle is formulated for bundles satisfying a certain orientation
compatibility property, and the corresponding components of the classical
solution space are promoted into a phase space. Avenues towards quantization
are briefly discussed.Comment: 33 pages, REVTeX v3.0, 3 figures in a separate PostScript fil
Measurement of the cross-section ratio sigma_{psi(2S)}/sigma_{J/psi(1S)} in deep inelastic exclusive ep scattering at HERA
The exclusive deep inelastic electroproduction of and
at an centre-of-mass energy of 317 GeV has been studied with the ZEUS
detector at HERA in the kinematic range GeV,
GeV and GeV, where is the photon virtuality, is the
photon-proton centre-of-mass energy and is the squared four-momentum
transfer at the proton vertex. The data for GeV were taken in
the HERA I running period and correspond to an integrated luminosity of 114
pb. The data for GeV are from both HERA I and HERA II
periods and correspond to an integrated luminosity of 468 pb. The decay
modes analysed were and for the
and for the . The cross-section ratio
has been measured as a function of
and . The results are compared to predictions of QCD-inspired
models of exclusive vector-meson production.Comment: 24 pages, 8 figure
Combined QCD and electroweak analysis of HERA data
A simultaneous fit of parton distribution functions (PDFs) and electroweak
parameters to HERA data on deep inelastic scattering is presented. The input
data are the neutral current and charged current inclusive cross sections which
were previously used in the QCD analysis leading to the HERAPDF2.0 PDFs. In
addition, the polarisation of the electron beam was taken into account for the
ZEUS data recorded between 2004 and 2007. Results on the vector and
axial-vector couplings of the Z boson to u- and d-type quarks, on the value of
the electroweak mixing angle and the mass of the W boson are presented. The
values obtained for the electroweak parameters are in agreement with Standard
Model predictions.Comment: 32 pages, 10 figures, accepted by Phys. Rev. D. Small corrections
from proofing process and small change to Fig. 12 and Table
Limits on the effective quark radius from inclusive scattering at HERA
The high-precision HERA data allows searches up to TeV scales for Beyond the
Standard Model contributions to electron-quark scattering. Combined
measurements of the inclusive deep inelastic cross sections in neutral and
charged current scattering corresponding to a luminosity of around 1
fb have been used in this analysis. A new approach to the beyond the
Standard Model analysis of the inclusive data is presented; simultaneous
fits of parton distribution functions together with contributions of "new
physics" processes were performed. Results are presented considering a finite
radius of quarks within the quark form-factor model. The resulting 95% C.L.
upper limit on the effective quark radius is cm.Comment: 10 pages, 4 figures, accepted by Phys. Lett.
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