title: Stratified Approximation Results in Singular Spaces
creator: Listiyanto, -
subject: ddc-500
subject: 500 Natural sciences and mathematics
subject: ddc-510
subject: 510 Mathematics
description: Determining conditions under which a given map is close to a homeomorphism has been an  important problem in geometric topology. One of the major results related to the problem is  the α-Approximation  Theorem of Chapman and Ferry, which asserts that a small homotopy  equivalence between manifolds is small homotopic to a homeomorphism. In this context, the  smallness condition on a homotopy means that the size of the track covered by each point during  the homotopy is small when measured by an open cover of the target space. In proving  such a theorem, besides the original approach of ChapmanFerry  which uses some results from  topological surgery theory, there is another more geometric approach that is more suitable to  establish a similar theorem for classes of spaces more general than manifolds. This second approach,  due to Chapman himself, is to use controlled topological engulfing to prove a geometric  result on approximate fibrations called the Sucking Principle. The α-Approximation  Theorem  then follows from an application of this principle together with the Cell-Like  Approximation  Theorem of Siebenmann. In this thesis, based on previous work of B. Hughes, we develop various  tools that address the above approximation questions in a stratified setting of possibly singular  spaces. In particular, we establish the Stratified Radial Engulfing Theorem, the Stratified  Wrapping Up Theorem, the Stratified Handle Theorem, and the Stratified   gamma-Sucking  Theorem.  As a consequence we obtain a Stratified Sucking Theorem with unstratified polyhedral target  space.
date: 2021
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/29887/1/Dissertation_Listiyanto.pdf
identifier: DOI:10.11588/heidok.00029887
identifier: urn:nbn:de:bsz:16-heidok-298874
identifier:   Listiyanto, -  (2021) Stratified Approximation Results in Singular Spaces.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/29887/
rights: info:eu-repo/semantics/openAccess
rights: Please see front page of the work (Sorry, Dublin Core plugin does not recognise license id)
language: eng