# Pretzel links, mutation, and the slice-ribbon conjecture

@article{Aceto2018PretzelLM, title={Pretzel links, mutation, and the slice-ribbon conjecture}, author={Paolo Aceto and Min Hoon Kim and Junghwan Park and Arunima Ray}, journal={Mathematical Research Letters}, year={2018} }

Let p and q be distinct integers greater than one. We show that the 2-component pretzel link P(p,q,-p,-q) is not slice, even though it has a ribbon mutant, by using 3-fold branched covers and an obstruction based on Donaldson's diagonalization theorem. Combining this result with previous work of the first author we prove the slice-ribbon conjecture for 4-stranded 2-component pretzel links.

## 3 Citations

### Doubly Slice Montesinos Links

- MathematicsMichigan Mathematical Journal
- 2022

This paper compares notions of double sliceness for links. The main result is to show that a large family of 2-component Montesinos links are not strongly doubly slice despite being weakly doubly…

### The equivariant concordance group is not abelian

- Mathematics
- 2022

. We prove that the equivariant concordance group (cid:101) C is not abelian by exhibiting an inﬁnite family of nontrivial commutators.

### The equivariant concordance group is not abelian

- MathematicsBulletin of the London Mathematical Society
- 2022

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