Algebraic & Geometric Topology 9 (2009) 549–568

DOI: 10.2140/agt.2009.9.549

Abstract

We prove the projective plane RP² is an absolute extensor of a finite-dimensional metrizable space X if and only if the cohomological dimension mod 2 of X does not exceed 1. This solves one of the remaining difficult problems (posed by A N Dranishnikov) in Extension Theory. One of the main tools is the computation of the fundamental group of the function space Map(RPⁿ, RPⁿ⁺¹) (based at the inclusion) as being isomorphic to either Z₄ or Z₂ ⊕ Z₂ for n ≥ 1. Double surgery and the above fact yield the proof.

Keywords

absolute extensor, cohomological dimension, covering dimension, extension dimension, extension of maps, projective space

Mathematical Subject Classification

Primary: 54F45

Secondary: 54C65, 55M10

References

Publication

Received: 4 April 2007
Revised: 22 February 2009
Accepted: 23 February 2009
Published: 30 March 2009

Authors