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2018 Contractibility of manifolds by means of stochastic flows
Marcio Colombo Fenille
Topol. Methods Nonlinear Anal. 52(2): 613-629 (2018). DOI: 10.12775/TMNA.2018.024

Abstract

Let $f$ be a map from a one-relator model two-complex $K_{\mathcal{P}}$ into the real projective plane. The composition $\varrho\circ f_{\#}$ of the homomorphism $f_{\#}$ induced by $f$ on fundamental groups with the action $\varrho$ of $\pi_1(\mathbb{R}\mathrm{P}^2)$ over $\pi_2(\mathbb{R}\mathrm{P}^2)$ provides a local integer coefficient system $f_{\#}^{\varrho}$ over $K_{\mathcal{P}}$. We prove that if the twisted integer cohomology group $H^2(K_{\mathcal{P}};_{f_{\#}^{\varrho}}\mathbb Z)=0$, then $f$ is homotopic to a non-surjective map. As an intermediary step for the proof, we show that if $H^2(K_{\mathcal{P}};_{\beta}\mathbb Z)=0$ for some local integer coefficient system $\beta$ over $K_{\mathcal{P}}$, then $K_{\mathcal{P}}$ is aspherical.

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Marcio Colombo Fenille. "Contractibility of manifolds by means of stochastic flows." Topol. Methods Nonlinear Anal. 52 (2) 613 - 629, 2018. https://doi.org/10.12775/TMNA.2018.024

Information

Published: 2018
First available in Project Euclid: 6 November 2018

MathSciNet: MR3915654
Digital Object Identifier: 10.12775/TMNA.2018.024

Rights: Copyright © 2018 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.52 • No. 2 • 2018
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