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Presentation complexes with the fixed point property

Iván Sadofschi Costa

Geometry & Topology 21 (2017) 1275–1283

We prove that there exists a compact two-dimensional polyhedron with the fixed point property and even Euler characteristic. This answers a question posed by R H Bing in 1969. We also settle a second question by Bing regarding the homotopy invariance of the fixed point property in low dimensions.

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fixed point property, two-dimensional complexes, efficient groups
Mathematical Subject Classification 2010
Primary: 55M20, 57M05, 57M20
Received: 15 February 2016
Revised: 1 March 2016
Accepted: 5 April 2016
Published: 17 March 2017
Proposed: Steve Ferry
Seconded: Ronald Stern, Peter Teichner
Iván Sadofschi Costa
Departamento de Matemática
Universidad de Buenos Aires
Ciudad Universitaria, Pabellón I
C1428EGA Buenos Aires