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

Banach Center Publications (1998)

- Volume: 42, Issue: 1, page 29-47
- ISSN: 0137-6934

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topCarter, J., and Saito, Masahico. "Surfaces in 3-space that do not lift to embeddings in 4-space." Banach Center Publications 42.1 (1998): 29-47. <http://eudml.org/doc/208814>.

@article{Carter1998,

abstract = {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 is immersed in general position. A similar example is shown to be liftable with an explicit lifting given. The problem of lifting is discussed in relation to the theory of surface braids. Finally, the orientations of the double point sets are studied in relation to the lifting problem.},

author = {Carter, J., Saito, Masahico},

journal = {Banach Center Publications},

keywords = {orientations; triple points; Boy's surface; knotted surfaces; surface; immersion; embedding; lifting},

language = {eng},

number = {1},

pages = {29-47},

title = {Surfaces in 3-space that do not lift to embeddings in 4-space},

url = {http://eudml.org/doc/208814},

volume = {42},

year = {1998},

}

TY - JOUR

AU - Carter, J.

AU - Saito, Masahico

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

JO - Banach Center Publications

PY - 1998

VL - 42

IS - 1

SP - 29

EP - 47

AB - 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 is immersed in general position. A similar example is shown to be liftable with an explicit lifting given. The problem of lifting is discussed in relation to the theory of surface braids. Finally, the orientations of the double point sets are studied in relation to the lifting problem.

LA - eng

KW - orientations; triple points; Boy's surface; knotted surfaces; surface; immersion; embedding; lifting

UR - http://eudml.org/doc/208814

ER -

## References

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