We give a minimal triangulation : S123S42
of the Hopf map h:S3S2 and use it to obtain a new construction of the 9-vertex complex projective plane. 相似文献
We prove that a ()-connected map from a compact PL -manifold to a generalized -manifold with the disjoint disks property, , is homotopic to a tame embedding. There is also a controlled version of this result, as well as a version for noncompact and proper maps that are properly ()-connected. The techniques developed lead to a general position result for arbitrary maps , , and a Whitney trick for separating submanifolds of that have intersection number 0, analogous to the well-known results when is a manifold.
Toric manifolds, a topological generalization of smooth projective toric varieties, are determined by an -dimensional simple convex polytope and a function from the set of codimension-one faces into the primitive vectors of an integer lattice. Their cohomology was determined by Davis and Januszkiewicz in 1991 and corresponds with the theorem of Danilov-Jurkiewicz in the toric variety case. Recently it has been shown by Buchstaber and Ray that they generate the complex cobordism ring. We use the Adams spectral sequence to compute the -theory of all toric manifolds and certain singular toric varieties.
The Bryant-Ferry-Mio-Weinberger surgery exact sequence for compact homology manifolds of dimension is used to obtain transversality, splitting and bordism results for homology manifolds, generalizing previous work of Johnston.
First, we establish homology manifold transversality for submanifolds of dimension : if is a map from an -dimensional homology manifold to a space , and is a subspace with a topological -block bundle neighborhood, and , then is homology manifold -cobordant to a map which is transverse to , with an -dimensional homology submanifold.
Second, we obtain a codimension splitting obstruction in the Wall -group for a simple homotopy equivalence from an -dimensional homology manifold to an -dimensional Poincaré space with a codimension Poincaré subspace with a topological normal bundle, such that if (and for only if) splits at up to homology manifold -cobordism.
Third, we obtain the multiplicative structure of the homology manifold bordism groups .
The National Ignition Facility (NIF) is a 192-beam laser
facility presently under construction at LLNL. When completed, NIF will be a
1.8-MJ, 500-TW ultraviolet laser system. Its missions are to obtain fusion
ignition and to perform high energy density experiments in support of the
US nuclear weapons stockpile. Four of the NIF beams have been commissioned
to demonstrate laser performance and to commission the target area including
target and beam alignment and laser timing. During this time, NIF
demonstrated on a single-beam basis that it will meet its performance goals
and demonstrated its precision and flexibility for pulse shaping, pointing,
timing and beam conditioning. It also performed four important experiments
for Inertial Confinement Fusion and High Energy Density Science. Presently,
the project is installing production hardware to complete the project in
2009 with the goal to begin ignition experiments in 2010. An integrated plan
has been developed including the NIF operations, user equipment such as
diagnostics and cryogenic target capability, and experiments and
calculations to meet this goal. This talk will provide NIF status, the plan
to complete NIF, and the path to ignition. 相似文献
Direct-drive inertial confinement fusion (ICF) is
expected to demonstrate high gain on the National Ignition Facility (NIF) in
the next decade and is a leading candidate for inertial fusion energy
production. The demonstration of high areal densities in hydrodynamically
scaled cryogenic DT or D2 implosions with neutron yields that are a
significant fraction of the “clean” 1-D predictions will validate the
ignition-equivalent direct-drive target performance on the OMEGA laser at
the Laboratory for Laser Energetics (LLE). This paper highlights the
recent experimental and theoretical progress leading toward achieving this
validation in the next few years.
The NIF will initially be configured for X-ray drive and with no beams
placed at the target equator to provide a symmetric irradiation of a
direct-drive capsule. LLE is developing the “polar-direct-drive” (PDD)
approach that repoints beams toward the target equator. Initial 2-D
simulations have shown ignition. A unique “Saturn-like” plastic ring
around the equator refracts the laser light incident near the equator toward
the target, improving the drive uniformity.
LLE is currently constructing the multibeam, 2.6-kJ/beam, petawatt laser
system OMEGA EP. Integrated fast-ignition experiments, combining the OMEGA
EP and OMEGA Laser Systems, will begin in FY08. 相似文献
We present a compared analysis of some properties of 3-Sasakian and 3-cosymplectic manifolds. We construct a canonical connection on an almost 3-contact metric manifold which generalises the Tanaka–Webster connection of a contact metric manifold and we use this connection to show that a 3-Sasakian manifold does not admit any Darboux-like coordinate system. Moreover, we prove that any 3-cosymplectic manifold is Ricci-flat and admits a Darboux coordinate system if and only if it is flat. 相似文献
We consider the quotient set of the set of nondegenerate affinor fields with respect to the action of the group of nowhere vanishing functions. This set is endowed with a structure of infinite-dimensional Lie group. On this Lie group, we construct an object of linear connection with respect to which all left-invariant vector fields are covariantly constant (the Cartan connection). 相似文献