Critical sets in 3-space
Publications Mathématiques de l'IHÉS, Volume 77 (1993), pp. 5-61.
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     author = {Grayson, Matthew and Pugh, Charles},
     title = {Critical sets in 3-space},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {5--61},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {77},
     year = {1993},
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     mrnumber = {94k:57049},
     language = {en},
     url = {http://archive.numdam.org/item/PMIHES_1993__77__5_0/}
}
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Grayson, Matthew; Pugh, Charles. Critical sets in 3-space. Publications Mathématiques de l'IHÉS, Volume 77 (1993), pp. 5-61. http://archive.numdam.org/item/PMIHES_1993__77__5_0/

M. Brown (1962), The monotone union of open n-cells is an open n-cell, Proc. AMS, 12, 812-814. | MR | Zbl

D. E. Christie (1944), Net homotopy for compacta, Trans. AMS, 56, 275-308. | MR | Zbl

R. Churchill (1972), Isolated invariant sets in compact metric spaces, JDE, 12, 330-352. | MR | Zbl

C. Conley (1978), Isolated invariant sets and the Morse index, CBMS regional conference series in math., number 38, AMS, Providence R.I. | MR | Zbl

M. E. Feign (1988), Separation properties of codimension-1 immersions, Topology, 27, 319-321. | MR | Zbl

R. H. Fox and E. Artin (1948), Some wild cells and spheres in three dimensional space, Annals of Math., 49, 979-990. | MR | Zbl

F. B. Fuller (1952), A note on trajectories in the solid torus, Annals of Math., 56, 438-439. | MR | Zbl

J. Harrison and C. Pugh (1990), A critical fractal circle, preprint, U. of California, Berkeley.

J. Hempel (1976), 3-manifolds, Annals of Math. Studies #86, Princeton U. Press, Princeton, N.J. | MR | Zbl

A. P. Morse (1939), The behaviour of a function on its critical set, Annals of Math., 40, 62-70. | JFM | Zbl

M. Morse (1934), The calculus of variations in the large, AMS Colloquium Publ. XVIII, N.Y. | JFM | Zbl

J. Munkres (1960), Obstructions to the smoothing of piecewise differentiable homeomorphisms, Annals of Math., 72, 521-554. | MR | Zbl

V. V. Nemytskii and V. V. Stepanov (1960), Qualitative theory of differential equations, Princeton U. Press, Princeton N. J. | MR | Zbl

Norton and Pugh (1991), Critical sets in the plane, Michigan J. Math, 38, 441-459. | MR | Zbl

C. Robinson (1976), personnal communication with C. Conley.

C. Robinson (1990), personnal communication with C. Pugh.

D. Rolfsen (1976), Knots and Links, Publish or Perish Press, Houston Texas. | MR | Zbl

M. Saito (1990), Links as critical sets, preprint, U. of Texas, Austin.

A. Sard (1942), The measure of the critical values of differentiable maps, Bull. AMS, 48, 883-890. | MR | Zbl

A. Shapiro and J. H. C. Whitehead (1958), A proof and extension of Dehn's Lemma, Bull. AMS, 64, 174-178. | MR | Zbl

M. Shub (1987), Global Stability of dynamical systems, Springer-Verlag, N.Y. | MR | Zbl

W. Thurston (1990), personnal communication with M. Grayson.

H. Whitney (1935), A function not constant on a connected set of critical points, Duke Math. J., 1, 514-517. | JFM | Zbl

R. L. Wilder (1930), A converse to the Jordan Brouwer Separation Theorem, Trans. AMS, 32, 632-657. | JFM | MR

F. W. Wilson, Jr. (1969), Smoothing derivatives of functions and applications, Trans. AMS, 139, 413-428. | MR | Zbl

F. W. Wilson, Jr. and J. Yorke (1973), Lyapunov functions and isolating blocks, JDE, 13, 106-123. | MR | Zbl