1 citations · 1 across the 2 of their papers we have counts for
5 papers
Depicting a generalized shift move in crown diagrams
J Williams
This paper gives a diagrammatic way to perform a generalized shift move on a crown diagram of a smooth 4-manifold. Applications include a simplified proof that if two crown diagram…
Existence of 2-parameter crossings, with applications
Jonathan D. Williams
A Morse 2-function is a generic smooth map from a manifold M of arbitrary finite dimension to a surface B. Its critical set maps to an immersed collection of cusped arcs in B. The…
Holomorphic polygons and smooth 4-manifold invariants
Jonathan D. Williams
Any smooth, closed oriented 4-manifold has a surface diagram of arbitrarily high genus g>2 that specifies it up to diffeomorphism. The goal of this paper is to prove the following…
Uniqueness of surface diagrams of smooth 4-manifolds
Jonathan D. Williams
In the author's earlier work there appeared a new way to specify any smooth closed 4-manifold by a surface diagram, which consists of an orientable surface decorated with simple cl…
The h-principle for broken Lefschetz fibrations
Jonathan D. Williams
It is known that an arbitrary smooth, oriented 4-manifold admits the structure of what is called a broken Lefschetz fibration. Given a broken fibration, there are certain modificat…