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All Outputs (7)

A specious unlinking strategy (2014)
Journal Article
Friedl, S., Nagel, M., & Powell, M. (2014). A specious unlinking strategy. Periodica Mathematica Hungarica, 69(2), 207-210. https://doi.org/10.1007/s10998-014-0063-y

We show that the following unlinking strategy does not always yield an optimal sequence of crossing changes: first split the link with the minimal number of crossing changes, and then unknot the resulting components.

Nonconcordant links with homology cobordant zero-framed surgery manifolds (2014)
Journal Article
Cha, J. C., & Powell, M. (2014). Nonconcordant links with homology cobordant zero-framed surgery manifolds. Pacific Journal of Mathematics, 272(1), 1-33. https://doi.org/10.2140/pjm.2014.272.1

We use topological surgery in dimension four to give sufficient conditions for the zero framed surgery manifold of a 3-component link to be homology cobordant to the 3-torus, which arises from zero framed surgery on the Borromean rings, via a topolog... Read More about Nonconcordant links with homology cobordant zero-framed surgery manifolds.

Shrinking of toroidal decomposition spaces (2014)
Journal Article
Kasprowski, D., & Powell, M. (2014). Shrinking of toroidal decomposition spaces. Fundamenta Mathematicae, 227(3), 271-296. https://doi.org/10.4064/fm227-3-3

Given a sequence of oriented links L^1,L^2,L^3,... each of which has a distinguished, unknotted component, there is a decomposition of the 3-sphere naturally associated to it, which is constructed as the components of the intersection of an infinite... Read More about Shrinking of toroidal decomposition spaces.

Embedded Morse Theory and Relative Splitting of Cobordisms of Manifolds (2014)
Journal Article
Borodzik, M., & Powell, M. (2016). Embedded Morse Theory and Relative Splitting of Cobordisms of Manifolds. Journal of Geometric Analysis, 26(1), 57-87. https://doi.org/10.1007/s12220-014-9538-6

We prove that an embedded cobordism between manifolds with boundary can be split into a sequence of right product and left product cobordisms, if the codimension of the embedding is at least two. This is a topological counterpart of the algebraic spl... Read More about Embedded Morse Theory and Relative Splitting of Cobordisms of Manifolds.

Covering link calculus and the bipolar filtration of topologically slice links (2014)
Journal Article
Cha, J. C., & Powell, M. (2014). Covering link calculus and the bipolar filtration of topologically slice links. Geometry & Topology, 18(3), 1539-1579. https://doi.org/10.2140/gt.2014.18.1539

The bipolar filtration introduced by T Cochran, S Harvey and P Horn is a framework for the study of smooth concordance of topologically slice knots and links. It is known that there are topologically slice 1–bipolar knots which are not 2–bipolar. For... Read More about Covering link calculus and the bipolar filtration of topologically slice links.

Concordance of links with identical Alexander invariants (2014)
Journal Article
Cha, J. C., Friedl, S., & Powell, M. (2014). Concordance of links with identical Alexander invariants. Bulletin of the London Mathematical Society, 46(3), 629-642. https://doi.org/10.1112/blms/bdu002

Davis showed that the topological concordance class of a link in the 3-sphere is uniquely determined by its Alexander polynomial for 2-component links with Alexander polynomial one. A similar result for knots with Alexander polynomial one was shown e... Read More about Concordance of links with identical Alexander invariants.