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Bounds for fixed points on surfaces. (English) Zbl 0903.55003

The notion of mutant and the Bestvina-Handel theory for graph maps is introduced, as well as the index bounds for graph maps and the index bounds on a surface. The index bounds are used to establish an equality for asymptotic invariants.

MSC:

55M20 Fixed points and coincidences in algebraic topology
57M15 Relations of low-dimensional topology with graph theory
20F65 Geometric group theory
57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
58C30 Fixed-point theorems on manifolds
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