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August 2020 Cohomology and the Bowditch Boundary
Jason F. Manning, Oliver H. Wang
Michigan Math. J. 69(3): 633-669 (August 2020). DOI: 10.1307/mmj/1596700822

Abstract

We give a group cohomological description of the Čech cohomology of the Bowditch boundary of a relatively hyperbolic group pair, generalizing a result of Bestvina–Mess about hyperbolic groups. In the case of a relatively hyperbolic Poincaré duality group pair, we show that the Bowditch boundary is a homology manifold. For a three-dimensional Poincaré duality pair, we recover the theorem of Tshishiku–Walsh stating that the boundary is homeomorphic to a two-sphere.

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Jason F. Manning. Oliver H. Wang. "Cohomology and the Bowditch Boundary." Michigan Math. J. 69 (3) 633 - 669, August 2020. https://doi.org/10.1307/mmj/1596700822

Information

Received: 19 July 2018; Revised: 15 January 2019; Published: August 2020
First available in Project Euclid: 6 August 2020

MathSciNet: MR4132607
Digital Object Identifier: 10.1307/mmj/1596700822

Subjects:
Primary: 20F67, 20J06, 57M07

Rights: Copyright © 2020 The University of Michigan

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Vol.69 • No. 3 • August 2020
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