Involutions whose fixed set has three or four components: a small codimension phenomenon
Contribuinte(s) |
Universidade Estadual Paulista (UNESP) |
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Data(s) |
27/04/2015
27/04/2015
2012
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Resumo |
Let T : M → M be a smooth involution on a closed smooth manifold and F = n j=0 F j the fixed point set of T, where F j denotes the union of those components of F having dimension j and thus n is the dimension of the component of F of largest dimension. In this paper we prove the following result, which characterizes a small codimension phenomenon: suppose that n ≥ 4 is even and F has one of the following forms: 1) F = F n ∪ F 3 ∪ F 2 ∪ {point}; 2) F = F n ∪ F 3 ∪ F 2 ; 3) F = F n ∪ F 3 ∪ {point}; or 4) F = F n ∪ F 3 . Also, suppose that the normal bundles of F n, F 3 and F 2 in M do not bound. If k denote the codimension of F n, then k ≤ 4. Further, we construct involutions showing that this bound is best possible in the cases 2) and 4), and in the cases 1) and 3) when n is of the form n = 4t, with t ≥ 1. |
Formato |
223-234 |
Identificador |
http://www.mscand.dk/article/view/15205 Mathematica Scandinavica, v. 110, n. 2, p. 223-234, 2012. 1903-1807 http://hdl.handle.net/11449/122703 6556211699447687 |
Idioma(s) |
eng |
Relação |
Mathematica Scandinavica |
Direitos |
closedAccess |
Palavras-Chave | #Involução; Fixed data; classe de Stiefel-Whitney; |
Tipo |
info:eu-repo/semantics/article |