Semi-free $R^1$ action and Bott map

• Дата: 2013
• Автори та афіліації: V. Sharko — Institute of Mathematics of the National Academy of Sciences of Ukraine, Kiev; D. Gol’cov — Institute of Mathematics of the National Academy of Sciences of Ukraine, Kiev
• Ключові слова: keywords
• Автори: Sharko, V., Gol’cov, D., Шарко, В., Гольцов, Д.
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Інститут математики НАН України 2013
• Онлайн доступ: https://trim.imath.kiev.ua/index.php/trim/article/view/311
• Назва журналу: Transactions of Institute of Mathematics of NAS of Ukraine

Let $M^{n}$ be a compact closed manifold of dimension at least 3. We study the $R^1$-Bott functions on $M^{n}$. Separately investigated $R^1$-invariant Bott functions on $M^{2n}$ with a semi-free circle action which has finitely many fixed points. The aim of this paper is to find exact values of minimal numbers of singular circles of some indices of $R^1$-invariant Bott functions on $M^{2n}$. Closely related to $ R^1 $-Bott function on a manifold $ M^n $ is a more flexible object, the decomposition of round handle of $ M^n $. In its turn, to study the round handles decomposition of $M^n $ we use a diagram, i.e. a graph which carries the information about the handles.