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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.

Copyright American Mathematical Society 1996

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Article Info

• ERA Amer. Math. Soc. 02 (1996), pp. 73-81
• Publisher Identifier: S 1079-6762(96)00010-8
• 1991 Mathematics Subject Classification. Primary 57N80, 57N37; Secondary 55R65, 57N40
• Received by the editors May 20, 1996
• Communicated by Walter Neumann
• Comments (When Available)

Bruce Hughes

Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240

E-mail address: hughescb@math.vanderbilt.edu

Supported in part by NSF Grant DMS-9504759.