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Martin Sleziak
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The Virtually Fibred ConjectureVirtually Fibred Conjecture, and related problems.
For a weaker definition of 3-manifold topology, I think the Andrews-Curtis conjectureAndrews-Curtis conjecture is a key problem. Also, anything which relates to the classification of non-simply-connected topological 4-manifolds, for instance problems related to knot and link concordance.

The Virtually Fibred Conjecture, and related problems.
For a weaker definition of 3-manifold topology, I think the Andrews-Curtis conjecture is a key problem. Also, anything which relates to the classification of non-simply-connected topological 4-manifolds, for instance problems related to knot and link concordance.

The Virtually Fibred Conjecture, and related problems.
For a weaker definition of 3-manifold topology, I think the Andrews-Curtis conjecture is a key problem. Also, anything which relates to the classification of non-simply-connected topological 4-manifolds, for instance problems related to knot and link concordance.

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Daniel Moskovich
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The Virtually Fibred Conjecture, and related problems.
For a weaker definition of 3-manifold topology, I think the Andrews-Curtis conjecture is a key problem. Also, anything which relates to the classification of non-simply-connected topological 4-manifolds, for instance problems related to knot and link concordance.