Neighborhoods in Stratified Spaces with Two Strata
  We develop a theory of tubular neighborhoods for the lower strata in manifold stratified spaces with two strata. In these topologically stratified spaces, manifold approximate fibrations and teardrops play the role that fibre bundles and mapping cylinders play in smoothly stratified spaces. Applications include the classification of neighborhood germs, the construction of exotic stratifications, a multiparameter isotopy extension theorem and an h-coborsism extension theorem. 
Bruce Hughes (Vanderbilt University), Laurence R. Taylor (University   of Notre Dame), Shmuel Weinberger (University of Chic...