On Homology Groups of a Subspace of Triangulations of the Two-Simplex with not More than 6 Subdivisional Boundary Vertices

On Homology Groups of a Subspace of Triangulations of the Two-Simplex with not More than 6 Subdivisional Boundary Vertices

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<p>We study homology groups of the space W˜<span style="line-height: 150%; font-family: 'Calibri','sans-serif'; font-size: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-lat...

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Main Author: S. I. Yablokova
Format: Article
Language:English
Published: Yaroslavl State University 2013-01-01
Series:Modelirovanie i Analiz Informacionnyh Sistem
Subjects:
триангуляция
симплекс
группа гомологий
Online Access:http://mais-journal.ru/jour/article/view/166
id doaj-84ecadcb648148f0ac0d215f950ac178
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spelling doaj-84ecadcb648148f0ac0d215f950ac1782020-11-25T01:40:06ZengYaroslavl State UniversityModelirovanie i Analiz Informacionnyh Sistem1818-10152313-54172013-01-01206142148160On Homology Groups of a Subspace of Triangulations of the Two-Simplex with not More than 6 Subdivisional Boundary VerticesS. I. Yablokova0Ярославский государственный университет им. П.Г. Демидова<p>We study homology groups of the space W˜<span style="line-height: 150%; font-family: 'Calibri','sans-serif'; font-size: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: RU; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;">₁</span>(∇<sup><span style="line-height: 150%; font-family: 'Calibri','sans-serif'; font-size: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">N</span></sup> ) of triangulations of the twodimensional simplex with vertices D<span style="line-height: 150%; font-family: 'Calibri','sans-serif'; font-size: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">₀</span>D₁D<span style="line-height: 150%; font-family: 'Calibri','sans-serif'; font-size: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">₂</span> endowed with a boundary subdivision with not more than 6 vertices in case when this boundary subdivision is extended to the interior of the simplex without adding new interior vertices. As a result, we obtain a theorem about the homology groups H<sub><span style="line-height: 150%; font-family: 'Calibri','sans-serif'; font-size: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">n</span></sub> in cases n = 0, . . . , 5.</p><p>The article is published in the author’s wording.</p>http://mais-journal.ru/jour/article/view/166триангуляциясимплексгруппа гомологий
collection DOAJ
language English
format Article
sources DOAJ
author S. I. Yablokova
spellingShingle S. I. Yablokova
On Homology Groups of a Subspace of Triangulations of the Two-Simplex with not More than 6 Subdivisional Boundary Vertices
Modelirovanie i Analiz Informacionnyh Sistem
триангуляция
симплекс
группа гомологий
author_facet S. I. Yablokova
author_sort S. I. Yablokova
title On Homology Groups of a Subspace of Triangulations of the Two-Simplex with not More than 6 Subdivisional Boundary Vertices
title_short On Homology Groups of a Subspace of Triangulations of the Two-Simplex with not More than 6 Subdivisional Boundary Vertices
title_full On Homology Groups of a Subspace of Triangulations of the Two-Simplex with not More than 6 Subdivisional Boundary Vertices
title_fullStr On Homology Groups of a Subspace of Triangulations of the Two-Simplex with not More than 6 Subdivisional Boundary Vertices
title_full_unstemmed On Homology Groups of a Subspace of Triangulations of the Two-Simplex with not More than 6 Subdivisional Boundary Vertices
title_sort on homology groups of a subspace of triangulations of the two-simplex with not more than 6 subdivisional boundary vertices
publisher Yaroslavl State University
series Modelirovanie i Analiz Informacionnyh Sistem
issn 1818-1015
2313-5417
publishDate 2013-01-01
description <p>We study homology groups of the space W˜<span style="line-height: 150%; font-family: 'Calibri','sans-serif'; font-size: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: RU; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;">₁</span>(∇<sup><span style="line-height: 150%; font-family: 'Calibri','sans-serif'; font-size: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">N</span></sup> ) of triangulations of the twodimensional simplex with vertices D<span style="line-height: 150%; font-family: 'Calibri','sans-serif'; font-size: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">₀</span>D₁D<span style="line-height: 150%; font-family: 'Calibri','sans-serif'; font-size: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">₂</span> endowed with a boundary subdivision with not more than 6 vertices in case when this boundary subdivision is extended to the interior of the simplex without adding new interior vertices. As a result, we obtain a theorem about the homology groups H<sub><span style="line-height: 150%; font-family: 'Calibri','sans-serif'; font-size: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">n</span></sub> in cases n = 0, . . . , 5.</p><p>The article is published in the author’s wording.</p>
topic триангуляция
симплекс
группа гомологий
url http://mais-journal.ru/jour/article/view/166
work_keys_str_mv AT siyablokova onhomologygroupsofasubspaceoftriangulationsofthetwosimplexwithnotmorethan6subdivisionalboundaryvertices
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