# Submanifolds of codimension two and homology equivalent manifolds

Sylvain E. Cappell; Julius L. Shaneson

Annales de l'institut Fourier (1973)

- Volume: 23, Issue: 2, page 19-30
- ISSN: 0373-0956

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topCappell, Sylvain E., and Shaneson, Julius L.. "Submanifolds of codimension two and homology equivalent manifolds." Annales de l'institut Fourier 23.2 (1973): 19-30. <http://eudml.org/doc/74124>.

@article{Cappell1973,

abstract = {In this paper new methods of studying codimension two embeddings of manifolds are outlined. Results are stated on geometric periodicity of knot cobordism. The group of local knots of a manifold in a 2-plane bundle is introduced and computed, and applied to $C^o$-close embeddings. General codimension two splitting theorems are discussed, with applications to equivariant knots and knot cobordism. A general existence theorem for P.L. (non-locally flat) embeddings is also given.The methods involve some new functors in Hermitian $K$-theory, denoted $\Gamma _n(\{\bf I\})$. Some of the results are stated in terms of these functors and a “Kunneth formula” for $\Gamma _n(\{\bf I\}\times Z)$ is indicated.},

author = {Cappell, Sylvain E., Shaneson, Julius L.},

journal = {Annales de l'institut Fourier},

language = {eng},

number = {2},

pages = {19-30},

publisher = {Association des Annales de l'Institut Fourier},

title = {Submanifolds of codimension two and homology equivalent manifolds},

url = {http://eudml.org/doc/74124},

volume = {23},

year = {1973},

}

TY - JOUR

AU - Cappell, Sylvain E.

AU - Shaneson, Julius L.

TI - Submanifolds of codimension two and homology equivalent manifolds

JO - Annales de l'institut Fourier

PY - 1973

PB - Association des Annales de l'Institut Fourier

VL - 23

IS - 2

SP - 19

EP - 30

AB - In this paper new methods of studying codimension two embeddings of manifolds are outlined. Results are stated on geometric periodicity of knot cobordism. The group of local knots of a manifold in a 2-plane bundle is introduced and computed, and applied to $C^o$-close embeddings. General codimension two splitting theorems are discussed, with applications to equivariant knots and knot cobordism. A general existence theorem for P.L. (non-locally flat) embeddings is also given.The methods involve some new functors in Hermitian $K$-theory, denoted $\Gamma _n({\bf I})$. Some of the results are stated in terms of these functors and a “Kunneth formula” for $\Gamma _n({\bf I}\times Z)$ is indicated.

LA - eng

UR - http://eudml.org/doc/74124

ER -

## References

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- [16] S. LOPEZ DE MEDRANO, «Involutions on Manifolds», Springer-Verlag, (1971).
- [17] S. LOPEZ DE MEDRANO, Invariant knots and surgery in codimension two, Actes du Congrès Int. des Mathématiciens Vol. 2. Gauthier-Villars, Paris, pp. 99-112. Zbl0231.57020MR54 #8653
- [18] J. L. SHANESON, Wall's Surgery obstruction groups for Z × G, Ann. of Math., 90 (1969), 296-334. Zbl0182.57303MR39 #7614
- [19] J. L. SHANESON, Surgery on 4-manifolds and topological transformation groups, In Procedings of the Amhearst Conference on Transformation groups (1970), to appear.
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