Tame topology - Misplaced Pages

Not to be confused with Tame manifold.

In mathematics, a tame topology is a hypothetical topology proposed by Alexander Grothendieck in his research program Esquisse d’un programme under the French name topologie modérée (moderate topology). It is a topology in which the theory of dévissage can be applied to stratified structures such as semialgebraic or semianalytic sets, and which excludes some pathological spaces that do not correspond to intuitive notions of spaces.

Some authors consider an o-minimal structure to be a candidate for realizing tame topology in the real case. There are also some other suggestions.

References

Alexander Grothendieck, 1984. "Esquisse d'un Programme", (1984 manuscript), finally published in Schneps and Lochak (1997, I), pp.5-48; English transl., ibid., pp. 243-283. MR 1483107
A'Campo, Ji & Papadopoulos 2016, § 1.
Dries, L. P. D. van den (1998). Tame Topology and O-minimal Structures. London Mathematical Society lecture note series, no. 248. Cambridge, New York, and Oakleigh, Victoria: Cambridge University Press. doi:10.1017/CBO9780511525919. ISBN 9780521598385.
Trimble, Todd (2011-06-12). "Answer to "A 'meta-mathematical principle' of MacPherson"". MathOverflow.
Ayala, David; Francis, John; Tanaka, Hiro Lee (5 February 2017). "Local structures on stratified spaces". Advances in Mathematics. 307: 903–1028. arXiv:1409.0501. doi:10.1016/j.aim.2016.11.032. ISSN 0001-8708. We conceive this package of results as a dévissage of stratified structures in the sense of Grothendieck.

A'Campo, Norbert; Ji, Lizhen; Papadopoulos, Athanase (2016). "On Grothendieck's tame topology". Handbook of Teichmüller Theory, Volume VI. IRMA Lectures in Mathematics and Theoretical Physics. Vol. 27. pp. 521–533. arXiv:1603.03016. doi:10.4171/161-1/17. ISBN 978-3-03719-161-3. S2CID 119693048.

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