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Manifold vs Symplectic - What's the difference?

manifold | symplectic |

In mathematics|lang=en terms the difference between manifold and symplectic

is that manifold is (mathematics) a topological space that looks locally like the "ordinary" euclidean space \mathbb{r}^n and is hausdorff while symplectic is (mathematics) describing the geometry of differentiable manifolds equipped with a closed, nondegenerate.

As adjectives the difference between manifold and symplectic

is that manifold is various in kind or quality, diverse while symplectic is (mathematics) describing the geometry of differentiable manifolds equipped with a closed, nondegenerate.

As a noun manifold

is (now historical) a copy made by the manifold writing process.

As an adverb manifold

is many times; repeatedly.

As a verb manifold

is to make manifold; multiply.

manifold

English

Alternative forms

* (l)

Etymology 1

From (etyl), from (etyl) .

Noun

(en noun)
  • (now historical) A copy made by the manifold writing process.
  • (mechanics) A pipe fitting or similar device that connects multiple inputs or outputs.
  • (US, regional, in the plural) The third stomach of a ruminant animal, an omasum.
  • * 1830 Anson, Somerset Co. Me., accessed 12 June 2007
    • My conjecture being right he will find the third stomach, or manifolds , the seat of difficulty.
  • (mathematics) A topological space that looks locally like the "ordinary" Euclidean space \mathbb{R}^n and is Hausdorff.
    • Derived terms
    * manifolder * (l) * (l)

    Adjective

    (en adjective)
  • Various in kind or quality, diverse
    • The manifold meanings of the simple English word 'set' are infamous among dictionary makers.
  • Many in number, numerous; multiple, multiplied.
  • Complicated.
  • Exhibited at diverse times or in various ways.
    • c1384 ... the manyfold grace of God. — I Petre 4:10 ( Wycliffe's Bible)
    1611 The manifold wisdom of God. — Ephesians 3:10]. ([[w:King James Bible])
    Derived terms
    * manifold writing

    Adverb

    (en adverb)
  • Many times; repeatedly.
  • * 1590 , Edmund Spenser, The Faerie Queene , I.xii:
    • when his daughter deare he does behold, / Her dearely doth imbrace, and kisseth manifold .

    Etymology 2

    From (etyl) manifolden, from (etyl) .

    Verb

    (en verb)
  • To make manifold; multiply.
  • (printing) To multiply or reproduce impressions of by a single operation.

    • symplectic

    English

    Adjective

    (-)
  • (mathematics) Describing the geometry of differentiable manifolds equipped with a closed, nondegenerate

    • External links

    * (wikipedia "symplectic")

    References

    * etymology of symplectic, by (Murray Gell-Mann). * The Symplectization of Science, Mark J. Gotay and , p. 13