Maps to the projective plane

Jerzy Dydak, Michael Levin

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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.

Original languageEnglish
Pages (from-to)549-568
Number of pages20
JournalAlgebraic and Geometric Topology
Volume9
Issue number1
DOIs
StatePublished - 1 Dec 2009

Keywords

  • Absolute extensor
  • Cohomological dimension
  • Covering dimension
  • Extension dimension
  • Extension of maps
  • Projective space

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