Публикации и препринты кафедры
высшей геометрии и топологии за 2002 г.
В.М.Бухштабер, Д.В.Лейкин.
Алгебры Ли, ассоциированные с сигма-функциями, и версальные деформации.
Русский: ps
2 стр.
Опубликовано: Успехи Матем.
Наук 57 (2002), вып.3, стр.145-146.
В.М.Бухштабер, Э.Рис.
Приложения фробениусовых n-гомоморфизмов.
Русский: ps
2 стр.
Опубликовано: Успехи Матем.
Наук 57 (2002), вып.1, стр.149-150.
И.А.Дынников.
Об одном отображении Янга-Бакстера и упорядочении Деорнуа.
Русский: ps
2 стр.
Опубликовано: Успехи Матем.
Наук 57 (2002), вып.3, стр.151-152.
И.А.Дынников.
Конечно определенные группы и полугруппы в теории узлов.
Русский: ps
(gzipped) tex
Английский: ps (gzipped)
tex
Опубликовано: Труды МИ РАН им. Стеклова 231 (2001).
Аннотация. In this paper we construct finitely presented semigroups
whose central elements are in one-to-one correspondence
with isotopy classes of non-oriented links in three-space. Solving the
word problem for those semigroups is equivalent to solving
the classification problem for links and tangles.
Also, we give a construction of finitely presented groups
containing the braid group as a subgroup.
Д.В.Миллионщиков.
Филиформные N-градуированные алгебры Ли.
Русский: ps
Английский: ps
2 стр.
arXiv.org e-Print archive: http://arXiv.org/abs/math.RA/0205042
Опубликовано: Успехи Матем.
Наук 57 (2002), вып.2, стр.197-198.
Д.В.Миллионщиков.
Когомологии с локальными коэффициентами солвмногообразий и задачи
теории Морса-Новикова.
Русский: ps
Английский: ps
2 стр.
arXiv.org e-Print archive: http://arXiv.org/abs/math.DG/0203067
Опубликовано: Успехи Матем.
Наук 57 (2002), вып.4, стр.183-184.
Ivan A. Dynnikov.
A new way to represent links, one-dimensional formalism and untangling
technology.
Английский: ps (gzipped)
41 стр.
Опубликовано: Acta Appl.
Math 69 (2002), no.3, 243-283.
Аннотация. An alternative link representation different from
planar diagrams is discussed.
Isotopy classes of unordered nonoriented links are
realized as central elements of a monoid presented explicitly
by a finite number of generators and relations.
A new partial algorithm for recognizing is constructed.
Experiments show that the algorithm allows to untangle
unknots whose planar diagram has hundreds of crossings.
Here `to untangle' means `to find an isotopy to the circle'
Victor Nistor, Evgenij Troitsky
An index for gauge-invariant operators
and the Dixmier-Douady invariant.
Английский: ps (gzipped)
28 стр.
arXiv.org e-Print archive: http://ru.arXiv.org/abs/math.KT/0201207
Abstract. Let $\GR \to B$ be a bundle of compact Lie groups
acting on a fiber bundle $Y \to B$. In this paper we introduce
and study gauge-equivariant $K$-theory groups $K_\GR^i(Y)$.
These groups satisfy the usual properties of the
equivariant $K$-theory groups, but also some new
phenomena arise due to the topological non-triviality of the
bundle $\GR \to B$. As an application, we define a
gauge-equivariant index for a family of elliptic operators
$(P_b)_{b \in B}$ invariant with respect to
the action of $\GR \to B$, which, in this approach, is an element of
$K_\GR^0(B)$. We then give another definition of
the gauge-equivariant index as an element of
$K_0(C^*(\GR))$, the $K$-theory group of the Banach
algebra $C^*(\GR)$. We prove that
$K_0(C^*(\GR))\simeq K^0_\GR(\GR)$ and that the two
definitions of the gauge-equivariant index are equivalent. The algebra
$C^*(\GR)$ is the algebra of continuous sections of a
certain field of $C^*$-algebras with non-trivial
Dixmier-Douady invariant. The gauge-equivariant $K$-theory
groups are thus examples of twisted $K$-theory
groups, which have recently proved themselves
useful in the study of Ramond-Ramond fields.
Sergey P. Novikov.
On the exotic De-Rham cohomology.
Perturbation theory as a spectral sequence.
Английский: ps (gzipped)
18 стр.
arXiv.org e-Print archive: http://ru.arXiv.org/abs/math-ph/0201019
Abstract. This work is dedicated to some new exotic
homological constructions associated with the different Morse-type
inequalities for differential forms and vector fields.
It contains also survey of ideas developed by the present
author in 1986 for this goal.
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