965 research outputs found
Non-factorial nodal complete intersection threefolds
We give a bound on the minimal number of singularities of a nodal projective
complete intersection threefold which contains a smooth complete intersection
surface that is not a Cartier divisor
Adelic Integrable Systems
Incorporating the zonal spherical function (zsf) problems on real and
-adic hyperbolic planes into a Zakharov-Shabat integrable system setting, we
find a wide class of integrable evolutions which respect the number-theoretic
properties of the zsf problem. This means that at {\it all} times these real
and -adic systems can be unified into an adelic system with an -matrix
which involves (Dirichlet, Langlands, Shimura...) L-functions.Comment: 23 pages, uses plain TE
Topological properties of spin-triplet superconductors and the Fermi surface topology in the normal state
We report intimate relations between topological properties of full gapped
spin-triplet superconductors with time-reversal invariance and the Fermi
surface topology in the normal states. An efficient method to calculate the Z2
invariants and the winding number for the spin-triplet superconductors is
developed, and connections between these topological invariants and the Fermi
surface structures in the normal states are pointed out. We also obtain a
correspondence between the Fermi surface topology and gapless surface states in
the superconducting states. The correspondence is inherent to spin-triplet
superconductivity.Comment: 14 pages, 2 figures, 1 table, a table was adde
Compactification, topology change and surgery theory
We study the process of compactification as a topology change. It is shown
how the mediating spacetime topology, or cobordism, may be simplified through
surgery. Within the causal Lorentzian approach to quantum gravity, it is shown
that any topology change in dimensions may be achieved via a causally
continuous cobordism. This extends the known result for 4 dimensions.
Therefore, there is no selection rule for compactification at the level of
causal continuity. Theorems from surgery theory and handle theory are seen to
be very relevant for understanding topology change in higher dimensions.
Compactification via parallelisable cobordisms is particularly amenable to
study with these tools.Comment: 1+19 pages. LaTeX. 9 associated eps files. Discussion of disconnected
case adde
Connectedness properties of the set where the iterates of an entire function are unbounded
We investigate the connectedness properties of the set I+(f) of points where the iterates of an entire function f are unbounded. In particular, we show that I+(f) is connected whenever iterates of the minimum modulus of f tend to ∞. For a general transcendental entire function f, we show that I+(f)∪ \{\infty\} is always connected and that, if I+(f) is disconnected, then it has uncountably many components, infinitely many of which are unbounded
Attracting domains of maps tangent to the identity whose only characteristic direction is non-degenerate
We prove that a holomorphic fixed point germ in two complex variables,
tangent to the identity, and whose only characteristic direction is
non-degenerate, has a domain of attraction on which the map is conjugate to a
translation. In the case of a global automorphism, the corresponding domain of
attraction is a Fatou-Bieberbach domain
Quantum Degenerate Systems
Degenerate dynamical systems are characterized by symplectic structures whose
rank is not constant throughout phase space. Their phase spaces are divided
into causally disconnected, nonoverlapping regions such that there are no
classical orbits connecting two different regions. Here the question of whether
this classical disconnectedness survives quantization is addressed. Our
conclusion is that in irreducible degenerate systems --in which the degeneracy
cannot be eliminated by redefining variables in the action--, the
disconnectedness is maintained in the quantum theory: there is no quantum
tunnelling across degeneracy surfaces. This shows that the degeneracy surfaces
are boundaries separating distinct physical systems, not only classically, but
in the quantum realm as well. The relevance of this feature for gravitation and
Chern-Simons theories in higher dimensions cannot be overstated.Comment: 18 pages, no figure
Localized Exotic Smoothness
Gompf's end-sum techniques are used to establish the existence of an infinity
of non-diffeomorphic manifolds, all having the same trivial
topology, but for which the exotic differentiable structure is confined to a
region which is spatially limited. Thus, the smoothness is standard outside of
a region which is topologically (but not smoothly) ,
where is the compact three ball. The exterior of this region is
diffeomorphic to standard . In a
space-time diagram, the confined exoticness sweeps out a world tube which, it
is conjectured, might act as a source for certain non-standard solutions to the
Einstein equations. It is shown that smooth Lorentz signature metrics can be
globally continued from ones given on appropriately defined regions, including
the exterior (standard) region. Similar constructs are provided for the
topology, of the Kruskal form of the Schwarzschild
solution. This leads to conjectures on the existence of Einstein metrics which
are externally identical to standard black hole ones, but none of which can be
globally diffeomorphic to such standard objects. Certain aspects of the Cauchy
problem are also discussed in terms of \models which are
``half-standard'', say for all but for which cannot be globally
smooth.Comment: 8 pages plus 6 figures, available on request, IASSNS-HEP-94/2
K-orbit closures on G/B as universal degeneracy loci for flagged vector bundles with symmetric or skew-symmetric bilinear form
We use equivariant localization and divided difference operators to determine
formulas for the torus-equivariant fundamental cohomology classes of -orbit
closures on the flag variety , where G = GL(n,\C), and where is one
of the symmetric subgroups O(n,\C) or Sp(n,\C). We realize these orbit
closures as universal degeneracy loci for a vector bundle over a variety
equipped with a single flag of subbundles and a nondegenerate symmetric or
skew-symmetric bilinear form taking values in the trivial bundle. We describe
how our equivariant formulas can be interpreted as giving formulas for the
classes of such loci in terms of the Chern classes of the various bundles.Comment: Minor revisions and corrections suggested by referees. Final version,
to appear in Transformation Group
Cohomological non-rigidity of generalized real Bott manifolds of height 2
We investigate when two generalized real Bott manifolds of height 2 have
isomorphic cohomology rings with Z/2 coefficients and also when they are
diffeomorphic. It turns out that cohomology rings with Z/2 coefficients do not
distinguish those manifolds up to diffeomorphism in general. This gives a
counterexample to the cohomological rigidity problem for real toric manifolds
posed in \cite{ka-ma08}. We also prove that generalized real Bott manifolds of
height 2 are diffeomorphic if they are homotopy equivalent
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