Thomas Kindred

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math.GT2026

Spanning solids and Murasugi sum in dimension four

Homayun Karimi, Seungwon Kim, Thomas Kindred +2

We study various constructions of spanning solids for knotted surfaces in the 4-sphere. In particular, we consider a 4-dimensional analogue of Murasugi sum, which we use to define…

math.GT2024

Kink-equivalence of matrices, spanning surfaces, 4-manifolds, and quadratic forms

Hugh Howards, Thomas Kindred, W. Frank Moore +1

All checkerboard surfaces for a given knot in $S^{3}$ are related by isotopy and "kinking" and "unkinking" moves, which change the surfaces' Goeritz matrices like this: $G\leftrighta…

math.GT2024

How essential is a spanning surface?

Thomas Kindred

Gabai proved that any plumbing, or Murasugi sum, of $I ¨ _{1}$ -essential Seifert surfaces is also $I ¨ _{1}$ -essential, and Ozawa extended this result to unoriented spanning surfaces. We s…