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This article is available for purchase or by subscription. See below.
Abstract
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We study surface representatives of homology classes of finite complexes
which minimize certain complexity measures, including their genus
and Euler characteristic. Our main result is that, up to surgery at
nullhomotopic curves, minimizers are homotopic to cellwise coverings of the
–skeleton.
From this we conclude that the minimizing problem is in
general algorithmically undecidable, but can be solved for
–dimensional
complexes.
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Keywords
minimal genus, two-complex, undecidability
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Mathematical Subject Classification
Primary: 57R95
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Publication
Received: 19 October 2020
Revised: 3 March 2021
Accepted: 29 March 2021
Published: 25 August 2022
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