∫_x^hx(g^*α-α)

2011/05/04 by Światosław R. Gal, Gal, Światosław R., Jarek Kędra +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #math.DS #math.GR #math.GT

paper · pdf · doi:10.48550/arxiv.1105.0825

openalex publication_date 2011/05/04 · arxiv created 2011/10/06 · arxiv updated 2011/10/07 · openalex created_date 2022/08/28 · openalex updated_date 2026/07/28

Abstract

Let X be a connected topological space admitting a universal cover. Let a be a degree one cohomology class on X. We define and study a two-cocycle on a group acting on X by homeomorphisms preserving the class a. We use this cocycle to investigate group actions on X. For example, we show that if an action preserves a Borel probability measure on X then the cocycle is cohomologically trivial. Under various assumptions on a homeomorphism g, we prove that it is undistorted in Homeo(X,a). In particular, we introduce a local rotation number of a homeomorphism and prove that a homeomorphism with non-constant local rotation number is undistorted.

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