Involutions in mapping class groups of non-orientable surfaces.

Blazek Szepietowski

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Surfaces in 3-space that do not lift to embeddings in 4-space

J. Carter, Masahico Saito (1998)

Banach Center Publications

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A necessary and sufficient condition for an immersed surface in 3-space to be lifted to an embedding in 4-space is given in terms of colorings of the preimage of the double point set. Giller's example and two new examples of non-liftable generic surfaces in 3-space are presented. One of these examples has branch points. The other is based on a construction similar to the construction of Giller's example in which the orientation double cover of a surface with odd Euler characteristic...

Embedded surfaces in the 3-torus

Allan L. Edmonds (2008)

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Those maps of a closed surface to the three-dimensional torus that are homotopic to embeddings are characterized. Particular attention is paid to the more involved case when the surface is nonorientable.