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Morris Hirsch extended his work to immersions of general smooth manifolds. Along with John Nash's work on isometric immersions, the Hirsch–Smale immersion...

and Stephen Smale. His thesis was entitled Immersions of Manifolds. In 2012, he became a fellow of the American Mathematical Society. Hirsch had 23 doctoral...

 t2, ... , 0, tm). The Whitney trick was used by Stephen Smale to prove the h-cobordism theorem; from which follows the Poincaré conjecture in dimensions...

Stephen Smale. The statement is quite powerful, and the proof involves analysis. In topology it is often quoted — as in the Brouwer fixed-point theorem and...

Krantz 1987 Bell 1992 See: Hirsch 1994, p. 182, Theorem 1.9 Shastri 2011, p. 173, Theorem 6.4.3 See: Smale 1961 Milnor 1965 Hirsch 1994 Shastri 2011 Matsumoto...

Whitney–Graustein theorem. This was followed by the Nash–Kuiper isometric C1 embedding theorem and the Smale–Hirsch immersion theorem. Assume we want to...

immersions include: Whitney embedding theorem Whitney immersion theorem Nash embedding theorem Smale-Hirsch theorem Key tools in studying these maps are:...

Mishra & Sanghi (2006) Hirsch, Smale & Devaney (2003), pp. 303–305 Hirsch, Smale & Devaney (2003), pp. 306+307 Hirsch, Smale & Devaney (2003), pp. 307–308...

embedding for 2m < n; these are the Whitney immersion theorem and Whitney embedding theorem. Stephen Smale expressed the regular homotopy classes of immersions...

theorem Freudenthal suspension theorem Hurewicz theorem Künneth theorem Lefschetz fixed-point theorem Leray–Hirsch theorem Poincaré duality theorem Seifert–van...

Nash and Kuiper's isometric embedding theorems and the results on immersions by Morris Hirsch and Stephen Smale, Gromov introduced the h-principle in...

equations. New York-Toronto-London: McGraw-Hill Book Company, Inc. Hirsch, Morris W. and Smale, Stephen (1974). Differential equations, dynamical systems, and...

The implicit function theorem: history, theory, and applications. Springer. p. Theorem 6.2.4. ISBN 978-1-4614-5980-4. Smale (1959). "Diffeomorphisms...

paths). These techniques were used in Raoul Bott's proof of his periodicity theorem. The analogue of Morse theory for complex manifolds is Picard–Lefschetz...

Simroth's organs – Heinrich Rudolf Simroth Smale's horseshoe – Stephen Smale Smale–Rössler theorem – Stephen Smale and Otto Rössler Smith–Waterman algorithm...

ergodic theorem has also had repercussions for dynamics. Stephen Smale made significant advances as well. His first contribution was the Smale horseshoe...

Linearization Theorem". Dynamical Systems: Differential Equations, Maps, and Chaotic Behaviour. London: Chapman & Hall. pp. 77–81. ISBN 0-412-39080-9. Hirsch, Morris;...

N < 4. This is still in agreement with Smale that any dynamics can occur for N ≥ 5. More specifically, Hirsch showed there is an invariant set C that...

problems has been cited by Stephen Smale as among the 18 greatest unsolved problems of the 21st century. In Smale's words, the third version of the problem...

problem (Ernest S. Croot III, 2000) Lafforgue's theorem (Laurent Lafforgue, 1998) Fermat's Last Theorem (Andrew Wiles and Richard Taylor, 1995) Burr–Erdős...