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homotopy

noun
/həˈmɑtəpi/US

Etymology

From Ancient Greek ὁμός (homós, “same, similar”) + τόπος (tópos, “place”); earliest known use in print in 1922, Oswald Veblen, Analysis Situs.

  1. derived from ὁμός

Definitions

  1. A continuous deformation of one continuous function or map to another.

    • The concept of homotopy represents a formalisation of the intuitive idea of a smooth deformation of one curve into another.
    • An integer M is called an exponent for the torsion of an abelian group G if M * (torsion of G) = 0. We say that M is a homotopy exponent for a space X if M is an exponent for πₖ (X) for all k.
    • A graded Lie algebra arises from these maps via the Samelson product in homotopy, the so-called homotopy Lie algebra which is discussed below.

  2. The relationship between two continuous functions where homotopy from one to the other is…

    The relationship between two continuous functions where homotopy from one to the other is evident.

  3. Ellipsis of homotopy theory (“the systematic study of homotopies and their equivalence…

    Ellipsis of homotopy theory (“the systematic study of homotopies and their equivalence classes”).

  4. ›+ 2 more definitions

    1. A theory associating a system of groups with each topological space.

    2. A system of groups associated with a topological space.

The neighborhood

Derived

cohomotopy, homotopic, homotopy category, homotopy class, homotopy equivalence, homotopy equivalent, homotopy fiber, homotopy fibre, homotopy group, homotopy invariant, homotopy relative to a subspace, homotopy theory, homotopy type, linear homotopy, regular homotopy, straight-line homotopy

Vish — recursive loop

No curated loop yet for homotopy. Loops are being traced one word at a time while the ingestion pipeline matures.

sense glosses and etymology drawn from English Wiktionary · source · CC-BY-SA