On the Components of the Push-out Space with Certain Indices
Y. Kaya
article (Uluslararası, Hakemli) | Yazar(lar): Y. Kaya | Yıl: 2012 | Dergi/Kurum: RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA | İndeks: WOS.SCI — Özet: Given an immersion of a connected, m-dimensional manifold M without boundary into the Euclidean (m + k)-dimensional space, the idea of the push out sp
Given an immersion of a connected, m-dimensional manifold M without boundary into the Euclidean (m + k)-dimensional space, the idea of the push out space of the immersion under the assumption that immersion has flat normal bundle is introduced in [3]. It is known that the push-out space has finitely many path-connected components and each path-connected component can be assigned an integer called the index of the component. In this study, when M is compact, we give some new results on the push-out space. Especially it is proved that if the push-out space has a component with index 1, then the Euler number of M is 0 and if the immersion has a co-dimension 2, then the number of path-connected components of the push-out space with index (m - 1) is at most 2.