Geodesic
Geometric topology of stratified spaces
Hughes, Bruce1
1 Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
Electronic research announcements of the American Mathematical Society, Tome 02 (1996) no. 2, pp. 73-81.

Voir la notice de l'article provenant de la source American Mathematical Society

A theory of tubular neighborhoods for strata in manifold stratified spaces is developed. In these topologically stratified spaces, manifold stratified approximate fibrations and teardrops play the role that fibre bundles and mapping cylinders play in smoothly stratified spaces. Applications include a multiparameter isotopy extension theorem, neighborhood germ classification and a topological version of Thom’s First Isotopy Theorem.
DOI : 10.1090/S1079-6762-96-00010-8

Hughes, Bruce 1

1 Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240 
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Hughes, Bruce. Geometric topology of stratified spaces. Electronic research announcements of the American Mathematical Society, Tome 02 (1996) no. 2, pp. 73-81. doi : 10.1090/S1079-6762-96-00010-8. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-96-00010-8/

[1] Anderson, Douglas R., Hsiang, W. C. The functors 𝐾₋ᵢ and pseudo-isotopies of polyhedra Ann. of Math. (2) 1977 201 223

[2] Buchdahl, N. P., Kwasik, Sławomir, Schultz, Reinhard One fixed point actions on low-dimensional spheres Invent. Math. 1990 633 662

[3] Černavskiĭ, A. V. Local contractibility of the group of homeomorphisms of a manifold. Mat. Sb. (N.S.) 1969 307 356

[4] Chapman, T. A. Approximation results in topological manifolds Mem. Amer. Math. Soc. 1981

[5] Dovermann, Karl Heinz, Schultz, Reinhard Equivariant surgery theories and their periodicity properties 1990

[6] Edwards, Robert D., Kirby, Robion C. Deformations of spaces of imbeddings Ann. of Math. (2) 1971 63 88

[7] Goresky, Mark, Macpherson, Robert Stratified Morse theory 1988

[8] Hughes, C. Bruce Approximate fibrations on topological manifolds Michigan Math. J. 1985 167 183

[9] Hughes, C. B., Taylor, L. R., Williams, E. B. Bundle theories for topological manifolds Trans. Amer. Math. Soc. 1990 1 65

[10] Hughes, C. Bruce, Taylor, Laurence R., Williams, E. Bruce Manifold approximate fibrations are approximately bundles Forum Math. 1991 309 325

[11] Quinn, Frank Ends of maps. II Invent. Math. 1982 353 424

[12] Quinn, Frank Homotopically stratified sets J. Amer. Math. Soc. 1988 441 499

[13] Rourke, C. P., Sanderson, B. J. An embedding without a normal microbundle Invent. Math. 1967 293 299

[14] Siebenmann, L. C. Deformation of homeomorphisms on stratified sets. I, II Comment. Math. Helv. 1972

[15] Steinberger, Mark The equivariant topological 𝑠-cobordism theorem Invent. Math. 1988 61 104

[16] Steinberger, Mark, West, James Equivariant ℎ-cobordisms and finiteness obstructions Bull. Amer. Math. Soc. (N.S.) 1985 217 220

[17] Thom, R. Ensembles et morphismes stratifiés Bull. Amer. Math. Soc. 1969 240 284

[18] Verona, Andrei Stratified mappings—structure and triangulability 1984

[19] Weinberger, Shmuel Constructions of group actions: a survey of some recent developments 1985 269 298

[20] Weinberger, Shmuel The topological classification of stratified spaces 1994

[21] Whitney, Hassler Local properties of analytic varieties 1965 205 244

[22] Yan, Min The periodicity in stable equivariant surgery Comm. Pure Appl. Math. 1993 1013 1040

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