Outputs (3)

Symmetric chain complexes, twisted Blanchfield pairings, and knot concordance (2018)
Journal Article
Miller, A. N., & Powell, M. (2018). Symmetric chain complexes, twisted Blanchfield pairings, and knot concordance. Algebraic & geometric topology, 18(6), 3425-3476. https://doi.org/10.2140/agt.2018.18.3425

We give a formula for the duality structure of the 3 –manifold obtained by doing zero-framed surgery along a knot in the 3 –sphere, starting from a diagram of the knot. We then use this to give a combinatorial algorithm for computing the twisted Blan... Read More about Symmetric chain complexes, twisted Blanchfield pairings, and knot concordance.

Satellites and concordance of knots in 3-manifolds (2018)
Journal Article
Friedl, S., Nagel, M., Orson, P., & Powell, M. (2019). Satellites and concordance of knots in 3-manifolds. Transactions of the American Mathematical Society, 371(4), 2279-2306. https://doi.org/10.1090/tran/7313

Given a 3–manifold Y and a free homotopy class in [S1, Y ], we investigate the set of topological concordance classes of knots in Y × [0, 1] representing the given homotopy class. The concordance group of knots in the 3–sphere acts on this set. We sh... Read More about Satellites and concordance of knots in 3-manifolds.

Smooth and topological almost concordance (2018)
Journal Article
Nagel, M., Orson, P., Park, J., & Powell, M. (2019). Smooth and topological almost concordance. International Mathematics Research Notices, 2019(23), 7324-7355. https://doi.org/10.1093/imrn/rnx338

We investigate the disparity between smooth and topological almost concordance of knots in general 3-manifolds Y. Almost concordance is defined by considering knots in Y modulo concordance in Y × [0, 1] and the action of the concordance group of knot... Read More about Smooth and topological almost concordance.