Some counterexamples in surface homology
arXiv:2304.13256
Abstract
We present four counterexamples in surface homology. The first example shows that even if the loops inducing a homology basis intersect each other at most once, they still may separate the surface into two parts. The other three examples show some difficulties in working with minimal homology bases.
15 pages, 9 figures, extended version, Manuscripta Mathematica