Odd manifolds of small integral simplicial volume

Clara Loeh

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arXiv · 1509.00204

Odd manifolds of small integral simplicial volume

Clara Loeh

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Abstract

Integral simplicial volume is a homotopy invariant of oriented closed connected manifolds, defined as the minimal weighted number of singular simplices needed to represent the fundamental class with integral coefficients. We show that odd-dimensional spheres are the only manifolds with integral simplicial volume equal to 1. Consequently, we obtain an elementary proof that, in general, the integral simplicial volume of (triangulated) manifolds is not computable.

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BibTeX RIS

Clara Loeh. 2015-09-01. Odd manifolds of small integral simplicial volume. https://arxiv.org/abs/1509.00204

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