Stratifiye uzaylar üzerinde diferansiyel formlar

In this thesis, we studied the differential forms on stratified spaces by diffeological methods. A stratified space is a topological space that can be decomposed into pieces called strata which are required to fit together in a certain way. These spaces are not a manifold, and since there are no geometric definitions of concepts such as tangent bundles in singular spaces so differantial forms on these spaces are meaningless. However, in cases where the strata are manifold, it is possible to define the differential forms of these spaces on the regular parts by putting tube systems and appropriate retraction on these strata. In their study, Goresky-MacPherson described differential forms on stratified spaces by this method. Some of the tools we use in classical differential geometry can be meaningless and difficult in some cases due to the reasons mentioned above. For this reason, we will revise stratified spaces as diffeological spaces in order to use the tools that are meaningful on diffeological spaces. As a result, we will compare the differential forms on previously defined stratified spaces and the differential forms on diffeological spaces.