Homology, Homotopy and Applications

Volume 10 (2008)

Number 2

Involutions on 3-manifolds and self-dual, binary codes

Pages: 139 – 148

DOI: http://dx.doi.org/10.4310/HHA.2008.v10.n2.a7

Authors

Matthias Kreck (Hausdorff Research Institute for Mathematics, Bonn, Germany)

Volker Puppe (Fachbereich für Mathematik und Statistik, Universität Konstanz, Germany)

Abstract

We study a correspondence between orientation-reversing involutions on compact 3-manifolds with only isolated fixed points and self-dual, binary codes. We show in particular that every such code can be obtained from such an involution. We further relate doubly even codes to Pin-structures and Spin-manifolds.

Keywords

involution; 3-manifold; code; cohomology

2010 Mathematics Subject Classification

57M50, 57M60, 57R91, 94B05

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