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Surfaces in 4-manifolds and the surgery conjecture
Vyacheslav Krushkal
We give a survey of geometric approaches to the topological 4-dimensional surgery and 5-dimensional s-cobordism conjectures, with a focus on the study of surfaces in 4-manifolds. T…
On disk embedding up to s-cobordism
Vyacheslav Krushkal
The disk embedding lemma is a technique underlying the topological classification results in 4-manifold topology for good fundamental groups. The purpose of this paper is to develo…
Dwyer's filtration and topology of 4-manifolds
Vyacheslav Krushkal
Topological 4-dimensional surgery is conjectured to fail, in general, for free fundamental groups. M. Freedman and P. Teichner have shown that surgery problems with an arbitrary fu…
Embedding obstructions and 4-dimensional thickenings of 2-complexes
Vyacheslav S. Krushkal
The vanishing of Van Kampen's obstruction is known to be necessary and sufficient for embeddability of a simplicial n-complex into for , and it was recently shown…