Erratum to: A higher rank Lefschetz formula
نویسندگان
چکیده
منابع مشابه
A Lefschetz formula for higher rank
In this paper a Lefschetz formula is proved for the geodesic flow of a compact locally symmetric space. The flow is described in terms of actions of split tori of various dimensions and the geometric side of the Lefschetz formula is a sum over closed geodesics which correspond to a given torus. The cohomological side is given in terms of Lie algebra cohomology.
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We want to formulate an analogous statement for a flow Φ instead of a diffeomorphism. By looking at the local side of (1) the first idea would be to consider the fixed points of the flow and to assume they are nondegenerate. This way we get the Hopf formula expressing the Euler characteristic on the global side. More subtle information is supposed to be obtained by considering the closed orbits...
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We caution that # Fix(ψ) has to be interpreted with some care: it really denotes a fixed point count with multiplicities. A better way to phrase it as follows. Inside M ×M we have two submanifolds: the diagonal ∆ and the graph Γψ. We can then try to take # Fix(ψ) := ∆ · Γψ = “intersection number of ∆ and Γψ”. When ∆ and Γψ intersect transversely this intersection number coincides with the naïve...
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ژورنال
عنوان ژورنال: Journal of Fixed Point Theory and Applications
سال: 2010
ISSN: 1661-7738,1661-7746
DOI: 10.1007/s11784-010-0034-8