Hiroshima Mathematical Journal

Free involutions on torus semi-bundles and the Borsuk-Ulam Theorem for maps into $\mathbf{R}^n$

Alexandre Paiva Barreto, Daciberg Lima Gonçalves, and Daniel Vendrúscolo

Full-text: Open access

Abstract

In this article we classify the free involutions of every torus semi-bundle Sol 3-manifold. Moreover, we classify all the triples $M, \tau, \mathbf{R}^n$, where $M$ is as above, $\tau$ is a free involution on $M$, and $n$ is a positive integer, for which the Borsuk-Ulam Property holds.

Article information

Source
Hiroshima Math. J., Volume 46, Number 3 (2016), 255-270.

Dates
Received: 15 October 2014
Revised: 7 March 2016
First available in Project Euclid: 25 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1487991621

Digital Object Identifier
doi:10.32917/hmj/1487991621

Mathematical Reviews number (MathSciNet)
MR3614297

Zentralblatt MATH identifier
1362.55003

Subjects
Primary: 55M20: Fixed points and coincidences [See also 54H25]
Secondary: 57N10: Topology of general 3-manifolds [See also 57Mxx] 57S25: Groups acting on specific manifolds

Keywords
Sol 3-manifolds torus semi-bundle involutions covering space Borsuk-Ulam theorem

Citation

Paiva Barreto, Alexandre; Lima Gonçalves, Daciberg; Vendrúscolo, Daniel. Free involutions on torus semi-bundles and the Borsuk-Ulam Theorem for maps into $\mathbf{R}^n$. Hiroshima Math. J. 46 (2016), no. 3, 255--270. doi:10.32917/hmj/1487991621. https://projecteuclid.org/euclid.hmj/1487991621


Export citation