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Morse-Bott functions on manifolds with semi-free circle action
| Content Provider | Semantic Scholar |
|---|---|
| Author | Sharko, Vladimir V. |
| Copyright Year | 2009 |
| Abstract | 1. S1-invariant Morse-Bott functions Let W 2n be a closed smooth manifold. Suppose that W 2n admits a smooth semi-free circle action with finitely many fixed points. It is known that every isolated fixed point p of a semi-free S1-action has the following important property: near such a point the action is equivalent to a certain linear S1 = SO(2)-action on R2n. More precisely, for every isolated fixed point p there exist an open invariant neighborhood U of p and a diffeomorphism h from U to an open unit disk D in Cn centered at origin such that h conjugates the given S1-action on U to the S1-action on Cn with weight (1, . . . , 1). We will use both complex, (z1, . . . , zn), and real coordinates (x1, y1, . . . , xn, yn) on C n = R2n with zi = xi+ √ −1yi. The pair (U, h) will be called a standard chart at the point p. Let f : W 2n → R be a smooth S1-invariant function on the manifold W 2n. Denote by Σf the set of singular points of the function |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://dspace.nbuv.gov.ua/bitstream/handle/123456789/6331/41-Sharko.pdf?sequence=1 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
