Semi-free $R^1$ action and Bott map
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...
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| Datum: | 2013 |
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| Ключові слова: | keywords |
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2013
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| Online Zugang: | https://trim.imath.kiev.ua/index.php/trim/article/view/311 |
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| Назва журналу: | Transactions of Institute of Mathematics of NAS of Ukraine |
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Transactions of Institute of Mathematics of NAS of Ukraine| Zusammenfassung: | 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. |
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