Публикации и препринты кафедры
высшей геометрии и топологии за 2001 г.
Д.В.Миллионщиков.
Когомологии нильмногообразий и теорема Гончаровой.
Русский: ps
Английский (расширенный): ps
2 стр.
Опубликовано: Успехи Матем.
Наук 56 (2001), вып.4, стр.153-154.
Victor M. Buchstaber, Elmer G. Rees.
The Gelfand map and symmetric products.
Английский: ps (gzipped)
14 стр.
arXiv.org e-Print archive: http://ru.arXiv.org/abs/math.CO/0109122
Abstract. If A is an algebra of functions on X, there are many
cases when X can be regarded as included in Hom(A,C) as the set of ring
homomorphisms. In this paper the corresponding results for the symmetric
products of X are introduced. It is shown that the symmetric product
Symn(X) is included in Hom(A,C) as the set of those functions
that satisfy equations generalising f(xy)=f(x)f(y). These equations are
related to formulae introduced by Frobenius and, for the relevant A, they
characterise linear maps on A that are the sum of ring homomorphisms.
The main theorem is proved using an identity satisfied by partitions of
finite sets.
Petr G. Grinevich, Sergey P. Novikov.
Topological charge of the real periodic
finite-gap sine-Gordon solutions.
Английский: ps (gzipped)
30 стр.
arXiv.org e-Print archive: http://ru.arXiv.org/abs/math-ph/0111039
Abstract. An effective description of the inverse spectral data
corresponding to the real periodic and quasiperiodic
solutions for the sine-gordon equation is obtained. In particular,
the explicit formula for the so-called topological
charge of the solutions is found and proved. As it was
understood already 20 years ago, it is very hard to extract
any formula for this quantity from the Theta-functional
expressions. A new method was developed by the authors
for this goal. In the appendix 3 an analog of the
Fourier-Laurent integral transform on the Riemann surfaces is
defined, based on the constructions of the Soliton Theory.
It is a natural continuous analog of the discrete
Krichever-Novikov bases developed in the
late 80s for the needs of the Operator Quantization of String Theory.
Sergey P. Novikov.
A note on the real fermionic and bosonic quadratic forms: their
diagonalization and topological interpreation.
Английский: ps (gzipped)
9 стр.
arXiv.org e-Print archive: http://ru.arXiv.org/abs/math-ph/0110032
Abstract. We explain in this note how real fermionic and bosonic
quadratic forms can be effectively diagonalized. Nothing
like that exists for the general complex hermitian forms. Looks like this
observation was missed in the Quantum Field theoretical literature. The
present author observed it for the case of fermions in 1986 making some
topological work dedicated to the problem: how to construct Morse-type
inequalities for the generic real vector
fields? This idea also is presented in the note.
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