An obstruction to a knot being deform-spun via Alexander polynomials

@inproceedings{Budney2007AnOT,
  title={An obstruction to a knot being deform-spun via Alexander polynomials},
  author={Ryan Budney and Alexandra Mozgova},
  year={2007}
}
We show that if a co-dimension two knot is deform-spun from a lower-dimensional co-dimension 2 knot, there are constraints on the Alexander polynomials. In particular this shows, for all n, that not all co-dimension 2 knots in S n are deform-spun from knots in S n-1 . 
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References

SHOWING 1-10 OF 17 REFERENCES

Twisting spun knots

1. Introduction. In [5] Mazur constructed a homotopy 4-sphere which looked like one of the strongest candidates for a counterexample to the 4-dimensional Poincaré Conjecture. In this paper we show

Deforming twist-spun knots

In [151 Zeeman introduced the process of twist-spinning an n-knot to obtain an (n + I)-knot, and proved the remarkable theorem that a twist-spun knot is fibred. In [21 Fox described another

Knot modules. I

For a differentiable knot, i.e. an imbedding SI C S,+2, one can associate a sequence of modules (Aq) over the ring Z [t, I -l], which are the source of many classical knot invariants. If X is the

A family of embedding spaces

Let Emb(S^j,S^n) denote the space of C^infty-smooth embeddings of the j-sphere in the n-sphere. This paper considers homotopy-theoretic properties of the family of spaces Emb(S^j,S^n) for n >= j > 0.

Advanced Modern Algebra

This book is designed as a text for the first year of graduate algebra, but it can also serve as a reference since it contains more advanced topics as well. This second edition has a different

A Survey of Knot Theory

Some aspects of classical knot theory

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