TY  - GEN
KW  - stratifizierten Umfangungssatz
KW  -  stratifiziertes Aufrollen
KW  -  stratifizierten Henkelsatz
KW  -  stratifizierten
Ansaugesatz
ID  - heidok29887
Y1  - 2021///
TI  - Stratified Approximation Results in Singular Spaces
CY  - Heidelberg
AV  - public
N2  - 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 ?-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 ?-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.
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/29887/
A1  - Listiyanto, -
ER  -