René Thom and an Anticipated h-Principle

François Laudenbach ()
Additional contact information
François Laudenbach: Université de Nantes, Laboratoire de Mathématiques Jean Leray, UMR 6629 du CNRS

Chapter Chapter 12 in Geometry in History, 2019, pp 469-491 from Springer

Abstract: Abstract The first part of this chapter intends to present the role played by Thom in diffusing Smale’s ideas about immersion theory, at a time (1957) where they sound counterintuitive: it isclearlyimpossible to make the sphere inside out! Around a decade later, M. Gromov transformed Smale’s idea in what is now known as the h-principle. Here, the h stands for homotopy. Shortly after the astonishing discovery by Smale, Thom gave a lecture in Lille (1959) announcing a theorem which would deserve to be named a homologicalh-principle. The aim of our second part is to comment about this theorem which, at that time, was completely ignored by the topologists in Paris, but not in Leningrad. We explain Thom’s statement and comment about it. The first idea is combinatorial. A beautiful subdivision of the standard simplex emerges from Thom’s article. We connect it with the jiggling technique introduced by W. Thurston in his seminal work on foliations.

Keywords: Immersions; h-principle; Foliations; Jiggling; Haefliger structures (search for similar items in EconPapers)
Date: 2019
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-13609-3_12

Ordering information: This item can be ordered from
http://www.springer.com/9783030136093

DOI: 10.1007/978-3-030-13609-3_12

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().