Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 7, Number 2 (2007), 779-784.
On a conjecture of Gottlieb
We give a counterexample to a conjecture of D H Gottlieb and prove a strengthened version of it.
The conjecture says that a map from a finite CW–complex to an aspherical CW–complex with non-zero Euler characteristic can have non-trivial degree (suitably defined) only if the centralizer of the image of the fundamental group of is trivial.
As a corollary we show that in the above situation all components of non-zero degree maps in the space of maps from to are contractible.
We use –Betti numbers and homological algebra over von Neumann algebras to prove the modified conjecture.
Algebr. Geom. Topol., Volume 7, Number 2 (2007), 779-784.
Received: 26 April 2007
Accepted: 2 May 2007
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 55N99: None of the above, but in this section 55N25: Homology with local coefficients, equivariant cohomology 55N25: Homology with local coefficients, equivariant cohomology 54C35: Function spaces [See also 46Exx, 58D15]
Secondary: 57P99: None of the above, but in this section 55Q52: Homotopy groups of special spaces
Schick, Thomas; Thom, Andreas. On a conjecture of Gottlieb. Algebr. Geom. Topol. 7 (2007), no. 2, 779--784. doi:10.2140/agt.2007.7.779. https://projecteuclid.org/euclid.agt/1513796705