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nLab > Latest Changes: spectral geometry

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 8th 2013

    created a disambiguation page: spectral geometry

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeNov 11th 2013

    as seen by spectral triple (often inaccurately referred to “noncommutative geometry”)

    Why inaccurately ? Spectral triple is an approach from noncommutative geometry. Noncommutative geometry is a method, point of view. It can be applied to commutative world, and most important work in the subject that in fact aims to.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 11th 2013

    Inaccurately because the notion of spectral triple is much finer than the notion of NCG. Connes speaks of “metric NCG” sometimes to reflect this.

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeNov 11th 2013
    • (edited Nov 11th 2013)

    So in your opinion, the noncommutative geometry should denote just some vanilla topological version without any structures on the spaces ? Then call it noncommutative topology (not the best term, but for this discussion yes). Noncommutative geometry is IMHO (and in practice of many noncommutative geometers) a subject which looks at all kinds of geometrical structures on spaces locally associated to duals of noncommutative algebras of various kinds and categorical levels and possibly with additional structures.

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