Tame topology

In mathematics, a tame topology is a hypothetical topology proposed by Alexander Grothendieck in his research program Esquisse d’un programme[1] 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.[2]

Not to be confused with Tame manifold.

Some authors consider an o-minimal structure to be a candidate for realizing tame topology in the real case.[3][4] There are also some other suggestions.[5]

See also

References
  1. 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. MR1483107
  2. A'Campo, Ji & Papadopoulos 2016, § 1.
  3. Dries, L. P. D. van den (1998). Tame Topology and O-minimal Structures. London Mathematical Society lecture note series, no. 248. London Mathematical Society Lecture Note Series. Cambridge, New York, and Oakleigh, Victoria: Cambridge University Press. doi:10.1017/CBO9780511525919. ISBN 9780521598385.
  4. Trimble, Todd (2011-06-12). "Answer to "A 'meta-mathematical principle' of MacPherson"". MathOverflow.
  5. Ayala, David; Francis, John; Tanaka, Hiro Lee (5 February 2017). "Local structures on stratified spaces". Advances in Mathematics. 307: 903–1028. 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.
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