On the Components of the Push-out Space with Certain Indices

  • Yusuf Kaya

    Bülent Ecevit University, Zonguldak, Turkey


Given an immersion of a connected, mm-dimensional manifold MM without boundary into the Euclidean (m+k)(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 MM 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 11, then the Euler number of MM is 00 and if the immersion has a co-dimension 22, then the number of path connected components of the push-out space with index (m1)(m-1) 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. 1–16

DOI 10.4171/RSMUP/127-1