Presentation of immersed surface-links by marked graph diagrams

Kamada, Seiichi; Kawauchi, Akio; Kim, Ji-Eon; Lee, Sang Youl

doi:10.1142/s0218216518500529

Cited by 7 publications

(3 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[3,4,14,16,18,25,26,28]), methods of studying immersed surfaces diagrammatically have not been established as fully in the literature, aside from a few examples (see, e.g. [19] for a diagrammatic framework for representing immersed surfaces in R 4 via marked graph diagrams).…”

Section: Introductionmentioning

confidence: 99%

Band diagrams of immersed surfaces in 4-manifolds

Hughes¹,

Kim²,

Miller³

2021

Preprint

View full text Add to dashboard Cite

We study immersed surfaces in smooth 4-manifolds via singular banded unlink diagrams. Such a diagram consists of a singular link with bands inside a Kirby diagram of the ambient 4-manifold, representing a level set of the surface with respect to an associated Morse function. We show that every self-transverse immersed surface in a smooth, orientable, closed 4-manifold can be represented by a singular banded unlink diagram, and that such representations are uniquely determined by the ambient isotopy or equivalence class of the surface up to a set of singular band moves which we define explicitly. By introducing additional finger, Whitney, and cusp diagrammatic moves, we can use these singular band moves to describe homotopies or regular homotopies as well.Using these techniques, we introduce bridge trisections of immersed surfaces in arbitrary trisected 4-manifolds and prove that such bridge trisections exist and are unique up to simple perturbation moves. We additionally give some examples of how singular banded unlink diagrams may be used to perform computations or produce explicit homotopies of surfaces.

show abstract

Section: Introductionmentioning

confidence: 99%

Band diagrams of immersed surfaces in 4-manifolds

Hughes¹,

Kim²,

Miller³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…, Ω 8 , Ω 4 , Ω 6 } for surface-links embedded in R 4 introduced by K. Yoshikawa [Yos94], and recently extended by a set of three moves {Ω 9 , Ω 9 , Ω 10 } by S. Kamada, A. Kawauchi, J. Kim and S.Y. Lee [KKKL18] to include moves relating equivalent immersed surface-links.…”

Section: Introductionmentioning

confidence: 99%

Minimal generating set of planar moves for surfaces embedded in the four-space

Jablonowski

2021

J. Knot Theory Ramifications

View full text Add to dashboard Cite

show abstract

“…When m = 0, it is a trivial link with n components. H-trivial links are a generalization of trivial links, and play an important role in normal forms of immersed surface-links in R 4 [KK17,KKKL17].…”

Section: Introductionmentioning

confidence: 99%

On the group of ring motions of an H-trivial link

Damiani

Kamada

2019

Topology and its Applications

Self Cite

View full text Add to dashboard Cite

In this paper we compute a presentation for the group of ring motions of the split union of a Hopf link with Euclidean components and a Euclidean circle. A key part of this work is the study of a short exact sequence of groups of ring motions of general ring links in R 3 . This sequence allowed us to build the main result from the previously known case of the ring group with one component, which a particular case of the ring groups studied by Brendle and Hatcher. This work is a first step towards the computation of a presentation for groups of motions of H-trivial links with an arbitrary number of components.

show abstract

Presentation of immersed surface-links by marked graph diagrams

Cited by 7 publications

References 9 publications

Band diagrams of immersed surfaces in 4-manifolds

Band diagrams of immersed surfaces in 4-manifolds

Minimal generating set of planar moves for surfaces embedded in the four-space

On the group of ring motions of an H-trivial link

Contact Info

Product

Resources

About