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Geometric topology of stratified spaces
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## Geometric topology of stratified spaces

### Bruce Hughes

**Abstract.**
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.

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