Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
We present a survey of recent results concerned with generalizations of the classical Riemann-Hilbert transmission problem in the context of loop spaces. Specifically, we present a general formulation of a Riemann-Hilbert problem with values in an almost complex manifold and illustrate it by discussing two particular cases in more detail. First, using the generalized Birkhoff factorization theorem of A. Pressley and G. Segal we give a criterion of solvability for generalized Riemann-Hilbert problems with coefficients in the loop group of a compact Lie group. Next, we present a visual example of solution to a Riemann-Hilbert problem with values in the immersed loop space of three-dimensional sphere. Finally, we describe a geometric construction of Fredholm structures on loop groups and relate them to the canonical Fredholm structures on Kato Grassmannians.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
411-424
Opis fizyczny
Daty
wydano
2007
Twórcy
autor
- A. Razmadze Mathematical Institute, Georgian Academy of Sciences, M. Aleksidze Str. 1, Tbilisi 0193, Georgia
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-bc76-0-19