Given an immersion of a connected, -dimensional manifold withoutboundary into the Euclidean -dimensional space, the idea of the push-out space of the immersion under the assumption that immersion has flatnormal bundle is introduced in . It is known that the push-out space has finitely many path-connected components and eachpath-connected component can be assigned an integer called the index of thecomponent. In this study, when is compact, we give some new results onthe push-out space. Especially it is proved that if the push-out space has a component with index , then the Euler number of is and if the immersion has a co-dimension , then the number of pathconnected components of the push-out space with index is at most 2.
Cite this article
Yusuf Kaya, On the Components of the Push-out Space with Certain Indices. Rend. Sem. Mat. Univ. Padova 127 (2012), pp. 1–16DOI 10.4171/RSMUP/127-1