Skew Embeddings and Immersions of Manifolds into Euclidean Spaces in Codimension Two
Open Access
Author:
Tyurina, Yulia
Graduate Program:
Mathematics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
May 05, 2005
Committee Members:
Serge Tabachnikov, Committee Chair/Co-Chair Svetlana Katok, Committee Member Augustin Banyaga, Committee Member Aissa Wade, Committee Member Wojciech Makalowski, Committee Member
Embeddings and immersions of smooth closed oriented manifolds into Euclidean spaces of codimension two are investigated. An embedding (immersion) is skew if the embedded (immersed) manifold does not have a pair of parallel tangent spaces.
The author proves that an even-dimensional manifold cannot be skew embedded if its Euler characteristic is not zero, and provides an example
of a skew embedding of a torus into 4-dimensional Euclidean space. The author also proves that a skew embedding exists for a sphere of an arbitrary odd dimension. For immersions of two-dimensional oriented closed manifolds into
4-dimensional Euclidean space, the author gives an estimate from below for the number of parallel tangent spaces.
