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2009 Maps to the projective plane
Jerzy Dydak, Michael Levin
Algebr. Geom. Topol. 9(1): 549-568 (2009). DOI: 10.2140/agt.2009.9.549

Abstract

We prove the projective plane P2 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(Pn,Pn+1) (based at the inclusion) as being isomorphic to either 4 or 22 for n1. Double surgery and the above fact yield the proof.

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Jerzy Dydak. Michael Levin. "Maps to the projective plane." Algebr. Geom. Topol. 9 (1) 549 - 568, 2009. https://doi.org/10.2140/agt.2009.9.549

Information

Received: 4 April 2007; Revised: 22 February 2009; Accepted: 23 February 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1171.54026
MathSciNet: MR2491585
Digital Object Identifier: 10.2140/agt.2009.9.549

Subjects:
Primary: 54F45
Secondary: 54C65, 55M10

Rights: Copyright © 2009 Mathematical Sciences Publishers

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