# A note on stabilization heights of fiber surfaces and the Hopf invariants.

@article{Tagami2020ANO, title={A note on stabilization heights of fiber surfaces and the Hopf invariants.}, author={Keiji Tagami}, journal={arXiv: Geometric Topology}, year={2020} }

In this paper, we focus on the Hopf invariant and give an alternative proof for the unboundedness of stabilization heights of fiber surfaces, which was firstly proved by Baader and Misev.

## References

SHOWING 1-10 OF 27 REFERENCES

An Introduction to Knot Theory

- Mathematics
- 2001

This paper concentrates on the construction of invariants of knots, such as the Jones polynomials and the Vassiliev invariants, and the relationships of these invariants to other mathematics (such as…

On the stabilization height of fiber surfaces in S3

- Mathematics
- 2016

The stabilization height of a fiber surface in the 3-sphere is the minimal number of Hopf plumbing operations needed to attain a stable fiber surface from the initial surface. We show that families...

Some remarks on cabling, contact structures, and complex curves

- Mathematics
- 2008

We determine the relationship between the contact structure induced by a fibered knot, K, in the three-sphere and the contact structures induced by its various cables. Understanding this relationship…

On the stable equivalence of open books in three-manifolds

- Mathematics
- 2006

We show that two open books in a given closed, oriented three-manifold admit isotopic stabilizations, where the stabilization is made by successive plumbings with Hopf bands, if and only if their…

Minimal number of singular fibers in a Lefschetz fibration

- Mathematics
- 1998

There exists a (relatively minimal) genus g Lefschetz fibration with only one singular fiber over a closed (Riemann) surface of genus h iff g ≥ 3 and h ≥ 2. The singular fiber can be chosen to be…

Fibered knots with the same $0$-surgery and the slice-ribbon conjecture

- Mathematics
- 2015

Akbulut and Kirby conjectured that two knots with the same $0$-surgery are concordant. In this paper, we prove that if the slice-ribbon conjecture is true, then the modified Akbulut-Kirby's…

The second homology group of the mapping class group of an orientable surface

- Mathematics
- 1983

In I-7] Mumford shows that the Picard group P ic (~ ' ) is isomorphic to H2(F; 2~) and conjectures the latter is rank one, g>3 . We prove this below for g>5 . Another interpretation of this theorem…

Invariants of contact structures from open books

- Mathematics
- 2006

In this note we define three invariants of contact structures in terms of open books supporting the contact structures. These invariants are the support genus (which is the minimal genus of a page of…

Handlebody construction of Stein surfaces

- Mathematics
- 1998

The topology of Stein surfaces and contact 3-manifolds is studied by means of handle decompositions. A simple characterization of homeomorphism types of Stein surfaces is obtained-they correspond to…

Two theorems on the mapping class group of a surface

- Mathematics
- 1978

The mapping class group of a closed surface of genus > 3 is perfect. An infinite set of generators is given for the subgroup of maps that induce the identity on homology. Let Tg be the boundary of a…