Homotopy

This page is a sub-page of our page on Mathematical Concepts.

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Related KMR-pages:

Mathematics is Representation
Homology and Cohomology
Quotients
Topology
Duality
Dimension
Entropy
Uncertainty

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Representation: \, [ \, \mathrm{Lies} \, ]_{\, \mathrm{Truths}} \, \mapsto \, \left< \, \overset{\mathrm{Homotopic}}{\mathrm{Equivalence}} \, \right>_{\mathrm{Truths}} \,

Definition: Two lies \, L_1 \, and \, L_2 \, are equivalent if and only if
they can be transformed into each other by valid (= true) reasoning.

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Homotopy = Equivalence in the fundamental group of curves on a point under continuous parametric transformations.

Homotopy of Midgaard Snakes:

Characterizing (= describing the structure of) the different types of ‘tailbites’ that can be performed by the Midgård Snake in a given type of world.

The fundamental group of the torus is abelian:

Perelman and the Poincaré conjecture:

Thorsten Ekedahl giving a popular lecture (in Swedish) on this subject .

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