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

• 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
• ISSN: 1818-1015; 2313-5417

<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>(∇^{<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>} ) 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_{<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>} in cases n = 0, . . . , 5.</p><p>The article is published in the author’s wording.</p>