Involutions whose fixed set has three or four components: a small codimension phenomenon
- Autores: E. M. Barbaresco, Patricia E. Desideri
- Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 110, Nº 2, 2012, págs. 223-234
- Idioma: inglés
- Enlaces
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Resumen
Let T:M→M be a smooth involution on a closed smooth manifold and F=⋃nj=0Fj the fixed point set of T, where Fj 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=Fn∪F3∪F2∪{point}; 2) F=Fn∪F3∪F2; 3) F=Fn∪F3∪{point}; or 4) F=Fn∪F3. Also, suppose that the normal bundles of Fn, F3 and F2 in M do not bound. If k denote the codimension of Fn, 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.
