1,074 research outputs found
Toric Genera
Our primary aim is to develop a theory of equivariant genera for stably
complex manifolds equipped with compatible actions of a torus T^k. In the case
of omnioriented quasitoric manifolds, we present computations that depend only
on their defining combinatorial data; these draw inspiration from analogous
calculations in toric geometry, which seek to express arithmetic, elliptic, and
associated genera of toric varieties in terms only of their fans. Our theory
focuses on the universal toric genus \Phi, which was introduced independently
by Krichever and Loeffler in 1974, albeit from radically different viewpoints.
In fact \Phi is a version of tom Dieck's bundling transformation of 1970,
defined on T^k-equivariant complex cobordism classes and taking values in the
complex cobordism algebra of the classifying space. We proceed by combining the
analytic, the formal group theoretic, and the homotopical approaches to genera,
and refer to the index theoretic approach as a recurring source of insight and
motivation. The resultant flexibility allows us to identify several distinct
genera within our framework, and to introduce parametrised versions that apply
to bundles equipped with a stably complex structure on the tangents along their
fibres. In the presence of isolated fixed points, we obtain universal
localisation formulae, whose applications include the identification of
Krichever's generalised elliptic genus as universal amongst genera that are
rigid on SU-manifolds. We follow the traditions of toric geometry by working
with a variety of illustrative examples wherever possible. For background and
prerequisites we attempt to reconcile the literature of east and west, which
developed independently for several decades after the 1960s.Comment: 35 pages, LaTeX. In v2 references made to the index theoretical
approach to genera; rigidity and multiplicativity results improved;
acknowledgements adde
The identification of factors influencing choice of students of distance learning
The purpose of this advantage was to identify trust arising in students in the format of dictation training, their preferences in the learning process, factors affecting the choice of distant forms and motivateЦелью данного опроса являлось выявление трудностей, возникающих у обучающихся в формате дистанционного обучения, их предпочтения в процессе обучения, факторы, влияющие на выбор дистантной формы и мотиваци
Intersections of quadrics, moment-angle manifolds, and Hamiltonian-minimal Lagrangian embeddings
We study the topology of Hamiltonian-minimal Lagrangian submanifolds N in C^m
constructed from intersections of real quadrics in a work of the first author.
This construction is linked via an embedding criterion to the well-known
Delzant construction of Hamiltonian toric manifolds. We establish the following
topological properties of N: every N embeds as a submanifold in the
corresponding moment-angle manifold Z, and every N is the total space of two
different fibrations, one over the torus T^{m-n} with fibre a real moment-angle
manifold R, and another over a quotient of R by a finite group with fibre a
torus. These properties are used to produce new examples of Hamiltonian-minimal
Lagrangian submanifolds with quite complicated topology.Comment: 14 pages, published version (minor changes
Information and technical training of pedagogical personnel for work in the environment of distance learning
Рассматриваются проблемы информационно-технической подготовки педагогических кадров для работы в среде дистанционного обученияThe article deals with the problems of information and technical training of pedagogical personnel for work in a distance learning environmen
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