5 papers
How natural of a geometric operation is Murasugi sum?
Thomas Kindred
Gabai proved that any Murasugi sum of -essential Seifert surfaces is also -essential, and Ozawa extended this result to unoriented spanning surfaces. We show, however, th…
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…
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 are related by isotopy and (geometric) ``kinking" and ``unkinking" moves, which change matrices representing the surfaces' Gordo…
How essential is a spanning surface?
Thomas Kindred
We introduce new numerical invariants of a spanning surface , called the \emph{algebraic essence} and \emph{geometric essence} of , which measure how far is fr…
A simple proof of the Crowell-Murasugi theorem
Thomas Kindred
We give an elementary, self-contained proof of the theorem, proven independently in 1958-9 by Crowell and Murasugi, that the genus of an alternating knot equals half the breadth of…