Tame topology explained

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, 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.^{[2] [3]} There are also some other suggestions.^[4]

See also

• Thom's first isotopy lemma

References

• Book: 10.4171/161-1/17. On Grothendieck's tame topology . Handbook of Teichmüller Theory, Volume VI . IRMA Lectures in Mathematics and Theoretical Physics . 2016 . A'Campo . Norbert . Ji . Lizhen . Papadopoulos . Athanase . 27 . 521–533 . 1603.03016 . 978-3-03719-161-3 . 119693048 .

External links

• https://ncatlab.org/nlab/show/tame+topology

Notes and 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.
2. Book: Lou van den Dries

   . 10.1017/CBO9780511525919. Tame Topology and O-minimal Structures. London Mathematical Society lecture note series, no. 248. 1998 . Dries . L. P. D. van den . Lou van den Dries. 9780521598385. Cambridge University Press. Cambridge, New York, and Oakleigh, Victoria .

3. Web site: Todd . Trimble . Answer to "A 'meta-mathematical principle' of MacPherson" . MathOverflow . 2011-06-12.
4. Ayala . David . Francis . John . Tanaka . Hiro Lee . Local structures on stratified spaces . . 5 February 2017 . 307 . 903–1028 . 10.1016/j.aim.2016.11.032 . free . en . 0001-8708 . We conceive this package of results as a dévissage of stratified structures in the sense of Grothendieck.. 1409.0501 .