Genus (InstanceTopic, 3)

From Hi.gher. Space

Revision as of 22:57, 11 February 2014 by Hayate (Talk | contribs)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

In 3D, the genus of a shape is equal to how many "holes" it has that fully pierce the shape. For example, a sphere has genus 0, and a torus has genus 1.

In higher dimensions, it gets more complicated: with each new dimension, a new type of hole is possible. So each of the different four-dimensional torii have a pair of numbers as their "genus".

This is closely related to homology groups.