Genus (mathematics)

In mathematics,genus oftopological space such assurfacean integer representingmaximum numbercuts that can be made throughwithout renderingdisconnected. Thisroughly equivalent tonumberholesit, or handles on it.

For instance:

• A point, line, andsphere all have genus zero
• A torus has genus one, as doescoffee cup assolid object (solid torus),Möbius strip, andsymbol 0.
• The symbols 8B have genus two.
• A pretzel has genus three.

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In algebraic geometry there isdefinition forgenusany algebraic curve C. WhenfielddefinitionC iscomplex numbers,C has no singular points, then that definition coincides withtopological definition applied toRiemann surfaceC (its manifoldcomplex points). The definitionelliptic curve from algebraic geometrynon-singular curvegenus 1.

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in graph theory,genus ofgraph isinteger n such thatgraph can be drawn without crossing itself onsurfacen-handles. Thus,planar graph has genus 0. (can be drawn onsphere without self-crossing)