Essential surfaces in Seifert fiber spaces with singular surfaces

نویسندگان

چکیده

Two-sided incompressible surfaces in Seifert fiber spaces with isolated singular fibers are well-understood. Frohman [3] and Rannard [6] have shown that one-sided which either pseudo-horizontal or psuedo-vertical. We extend their result to characterise essential may surfaces, i.e., S1-foliated 3-manifolds fibered model neighbourhoods isomorphic a solid torus Klein bottle.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Minimal Surfaces in Seifert Fiber Spaces

This paper studies the minimal surfaces in Seifert fiber spaces equipped with their natural geometric structures. The minimal surfaces in these 3-manifolds are always either vertical, namely always tangent to fibers, or horizontal, always transverse to fibers. This gives a classification of injective surfaces in these manifolds, previously obtained by Waldhausen for embedded injective surfaces....

متن کامل

Knots with Infinitely Many Incompressible Seifert Surfaces

We show that a knot in S with an infinite number of incompressible Seifert surfaces contains a closed incompressible surface in its complement.

متن کامل

Unknotting Tunnels and Seifert Surfaces

Let K be a knot with an unknotting tunnel γ and suppose that K is not a 2-bridge knot. There is an invariant ρ = p/q ∈ Q/2Z, p odd, defined for the pair (K, γ). The invariant ρ has interesting geometric properties: It is often straightforward to calculate; e. g. for K a torus knot and γ an annulus-spanning arc, ρ(K, γ) = 1. Although ρ is defined abstractly, it is naturally revealed when K ∪ γ i...

متن کامل

Persistent laminations from Seifert surfaces

We show how an incompressible Seifert surface F for a knot K in S can be used to create an essential lamination LF in the complement of each of an in nite class of knots associated to F . This lamination is persistent for these knots; it remains essential under all non-trivial Dehn llings of the knot complement. This implies a very strong form of Property P for each of these knots.

متن کامل

Coordinate finite type invariant surfaces in Sol spaces

In the present paper, we study surfaces invariant under the 1-parameter subgroup in Sol space $rm Sol_3$. Also, we characterize the surfaces in $rm Sol_3$ whose coordinate functions of an immersion of the surface are eigenfunctions of the Laplacian $Delta$ of the surface.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Topology and its Applications

سال: 2023

ISSN: ['1879-3207', '0166-8641']

DOI: https://doi.org/10.1016/j.topol.2023.108627