Loading [MathJax]/jax/output/CommonHTML/jax.js
Видеотека
RUS  ENG    ЖУРНАЛЫ   ПЕРСОНАЛИИ   ОРГАНИЗАЦИИ   КОНФЕРЕНЦИИ   СЕМИНАРЫ   ВИДЕОТЕКА   ПАКЕТ AMSBIB  
Видеотека
Архив
Популярное видео

Поиск
RSS
Новые поступления






Международная конференция «Геометрия, топология, алгебра и приложения», посвященная 120-летию Бориса Николаевича Делоне (1890–1980)
20 августа 2010 г. 10:00, г. Москва
 


Sets of links of vertices of triangulated manifolds and combinatorial approach to Steenrod's problem on realisation of cycles

Alexander Gaifullin
Видеозаписи:
Windows Media 313.2 Mb
Flash Video 642.8 Mb
MP4 370.3 Mb

Количество просмотров:
Эта страница:682
Видеофайлы:258

Alexander Gaifullin



Аннотация: To each triangulated manifold one can assign the set of links of its vertices. The link of a vertex describes the local combinatorial structure of the triangulation in a neighbourhood of the vertex. Thus the set of links of vertices of a triangulation can be interpreted as the set of local combinatorial data characterizing the triangulation. We consider a compatibility problem for such local combinatorial data. This problem can be formulated in the following way. For a given set of combinatorial spheres, does there exist a triangulated manifold with such set of links of vertices? We are mostly interested in an oriented version of this problem. Our aim is to obtain a non-trivial sufficient condition for compatibility of a set of links of vertices. We shall describe an explicit construction that, under certain natural conditions, allows us to realise a multiple of a given set of oriented combinatorial spheres as the set of links of vertices of a combinatorial manifold.
Further, we are going to discuss an application of this construction to N. Steenrod's problem on realisation of cycles. It is well known that according to a result of R. Thom, any n-dimensional integral homology class z of any topological space X can be realised with some multiplicity by an image of an oriented smooth closed manifold Nn. Our new approach is based on an explicit combinatorial procedure for resolving singularities of a cycle. We give an explicit combinatorial construction that, for a given homology class z, yields a manifold Nn and its mapping to X which realises the class z with some multiplicity. Moreover, the obtained manifold Nn appears to be a finite-fold non-ramified covering over a very interesting special manifold Mn, which can be regarded either as an isospectral manifold of symmetric tridiagonal real (n+1)×(n+1)-matrices or as a small covering over a permutohedron.

Язык доклада: английский
 
  Обратная связь:
math-net2025_02@mi-ras.ru
 Пользовательское соглашение  Регистрация посетителей портала  Логотипы © Математический институт им. В. А. Стеклова РАН, 2025