2 results
Surgeries on iterated torus knots bounding rational homology 4-balls
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 66 / Issue 2 / May 2023
- Published online by Cambridge University Press:
- 23 June 2023, pp. 557-578
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We show that all large enough positive integral surgeries on algebraic knots bound a 4-manifold with a negative definite plumbing tree, which we describe explicitly. Then we apply the lattice embedding obstruction coming from Donaldson’s Theorem to classify the ones of the form
$S^3_n(T(p_1,k_1p_1+1; p_2, k_2p_2\pm 1))$ that also bound rational homology 4-balls.
On the structure of the Medvedev lattice
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- Journal:
- The Journal of Symbolic Logic / Volume 73 / Issue 2 / June 2008
- Published online by Cambridge University Press:
- 12 March 2014, pp. 543-558
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- June 2008
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We investigate the structure of the Medvedev lattice as a partial order. We prove that every interval in the lattice is either finite, in which case it is isomorphic to a finite Boolean algebra, or contains an antichain of size
. the size of the lattice itself. We also prove that it is consistent with ZFC that the lattice has chains of size . and in fact that these big chains occur in every infinite interval. We also study embeddings of lattices and algebras. We show that large Boolean algebras can be embedded into the Medvedev lattice as upper semilattices, but that a Boolean algebra can be embedded as a lattice only if it is countable. Finally we discuss which of these results hold for the closely related Muchnik lattice.
. the size of the lattice itself. We also prove that it is consistent with ZFC that the lattice has chains of size 