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Glossary

4 Topology's Twists and Turns

 

Box Diagram

Box diagrams, also known as gluing diagrams, are a convenient way to examine intrinsic topology.

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Configuration Space

A configuration space is a topological object that can be used to study the allowable states of a given system.

Configuration Space


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Euler Characteristic

The Euler characteristic is a topological invariant that relates a surface's vertices, edges, and faces.

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Extrinsic View

Extrinsic topology is the study of shape from an external perspective.

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Genus

Topological objects are categorized by their genus (number of holes). The genus of a surface is a feature of its global topology.

Genus


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Intrinsic View

Intrinsic topology is the study of shape from the perspective of being on the surface of the shape.

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Non-Orientability

If on a surface there is no meaningful way to tell an object's orientation (left or right handedness), the surface is said to be non-orientable.

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Irrational

Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.

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Topology

Topology, originally known as analysis situs—roughly, "geometry of position," seeks to describe what is fundamental about shape in general.

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Configuration SpaceTorus

The surface of a standard "donut shape" is known as a torus.

 

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