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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
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    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that Colourability is preserved under Reidemeister moves

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.A diagrammatic proof that each Reidemeister move preserves colourability is not equivalent to a proof that arbitrary sequences of such moves preserve it.
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    • 2.Preservation under finite composition requires an explicit inductive argument over sequence length, which the case-by-case diagrammatic check does not supply.
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    • 3.Without the inductive closure argument, the inference from local move-preservation to global invariance commits a fallacy of composition.
      ?

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    Reason for 2 of 2
    ?
    • 1.Colourability is defined relative to a modulus n, and the claim as stated suppresses this parameter, making it ambiguous across distinct colouring structures.
      ?

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    • 2.Reidemeister move preservation holds for Fox n-colourings only when n is fixed throughout; mixed or unspecified moduli can yield failures of preservation under type II moves.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.By Reidemeister's theorem, knot equivalence can be characterised by sequences of Reidemeister moves
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    • 2.Each individual Reidemeister move preserves colourability
      ?

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