Skip to content
Carmelics
TopicsThinkersChangesContributorsLoading account…

    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

    Navigate

    • Topics
    • Search
    • Recent Changes
    • Contribute
    • How It Works
    • Glossary
    • Thinkers
    • Contributors
    • About
    • Statistics
    • Terms
    • Privacy

    Database

    Statements
    —
    Perspectives
    —
    Topics
    —

    Press ? for keyboard shortcuts

    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    By Reidemeister's theorem, knot equivalence can be charac... — Carmelics
    Home/Modality & Possibility
    HistoryEditSee Inverse

    Part of a larger discussion

    Supports→Colourability is preserved under Reidemeister moves

    By Reidemeister's theorem, knot equivalence can be characterised by sequences of Reidemeister moves

    Modality & Possibility
    ?Rate how convincing each reason is below to see the overall strength.

    No one has weighed in yet. Be the first to share reasons for or against this statement.

    Sign in or register to share your perspective on this statement.

    Topics

    Modality & Possibility

    Related

    Colourability is preserved under Reidemeister movesEach individual Reidemeister move preserves colourability

    Similar

    Colourability is a knot invariant: if one diagram of a knot is coloura...76%

    Next step

    Based on where you are in your exploration

    Browse more in Modality & Possibility
    Related propositions within the same area of thought.
    The equivalence ∀x∃Xφ ≡ ∃Y∀xφ' holds in second-order logic, where Y ha...74%
    BF and CBF are theorems of SQML72%
    All theorems of CFL are provable in S5 when connexive implication A → ...71%

    Source

    AI-extracted
    SEP: epistemology-visual-thinking
    View source passageHide passage
    The reference to colours here is inessential. Colourability is in fact a specific case of a kind of combinatorial property known as mod \(p\) labelling (for \(p\) an odd prime). Colourability is a knot invariant in the sense that if one diagram of a knot is colourable every diagram of that knot and of any equivalent knot is colourable. (By Reidemeister’s theorem this can be proved by showing that each Reidemeister move preserves colourability.) A standard diagram of an unknot, a diagram without

    Details

    Type
    premise
    Perspectives
    0 (0 for, 0 against)
    Edits
    1 edit

    Open for perspectives

    This idea is waiting for its first supporting or challenging perspective.

    Share the first perspective