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The Georgicks of Virgil, with an English Translation and Notes Virgil, John Martyn Ipsi in defossis specubus secura sub alta Otia agunt terra, congestaque robora, Pierius says it is confecto in the Roman manuscript. And Tacitus also says the Germans used to make caves to defend them from the severity of winter, .

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AbeBooks Bookseller Since: May 31, Home R. Sher, R. Daverman Handbook of Geometric Topology. Stock Image. Handbook of Geometric Topology R. Published by North Holland, New Condition: New Hardcover. Save for Later. Discrete Fractional Calculus.

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Topology & Geometry - LECTURE 01 Part 01/02 - by Dr Tadashi Tokieda

Emily Riehl. The terminology "geometric topology" as far as I'm aware is a fairly recent historical phenomenon. The words used by topologists to describe their areas has had a fair bit of flux over the years. Before the mid's, algebraic topology was called combinatorial topology. I think the urge to use the phrase geometric topology began sometime after the advent of the h-cobordism theorem, and the observation that high-dimensional manifold theory, via a rather elaborate formulation can be largely turned into elaborate algebraic problems.

So there was a desire to have a term that held-together all the aspects of topology where these techniques either don't apply, or were not used or at least, not predominantly used. That's geometric topology. So 2, 3 and 4-dimensional manifold theory would be a big chunk of this area. But of course, even if high-dimensional manifold theory in principle reduces to algebra, that doesn't necessarily mean you want to use that reduction -- it may be too complicated to be useful.

So there are higher-order type high-dimensional manifold theory problems that don't fit the traditional reductions. Like say Vassiliev's work on spaces of knots. So this would also be considered geometric topology. Defining a subject by what it's not is kind of strange and artificial but all these subject-area definitions are kind of strange and artificial. I think the above-quoted blurbs also get at a key aspect of the area. Algebraic topology tends to be more focused on a broad set of tools.

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