A cylinder has genus 0, but a thick cylinder has genus 1. This gets me into wondering, since a Möbius strip has genus 1, would a thick Möbius strip have genus 2? I can't quite comprehend if the cuttings along a thick Möbius strip would be a closed curve or not.
2026-03-25 17:38:51.1774460331
Is a thick Möbius strip genus 2?
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A "thick" Möbius strip may be smoothed out into a torus, so it still has genus $1$.