Fixed points of local actions of nilpotent Lie groups on surfaces. (28th January 2016) - HIRSCH, MORRIS W.
Abstract : Let G be a connected nilpotent Lie group with a continuous local action on a real surface M, which might be non-compact or have non-empty boundary [STIX]x2202M . The action need not be smooth. Let [STIX]x1D711 be the local flow on M induced by the action of some one-parameter subgroup. Assume K is a compact set of fixed points of [STIX]x1D711 and U is a neighborhood of K containing no other fixed points. Theorem. If the Dold fixed-point index of [STIX]x1D711_t|U is non-zero for sufficiently small t>0, then Fix(G)K≠ .