Topological triviality of smoothly knotted surfaces in 4-manifolds
Hee Jung Kim, Daniel Ruberman
Abstract
Some generalizations and variations of the Fintushel-Stern rim surgery are known to produce smoothly knotted surfaces. We show that if the fundamental groups of their complements are cyclic, then these surfaces are topologically unknotted. Using a twist-spinning construction from high-dimensional knot theory, we construct examples of knotted surfaces whose complements have cyclic fundamental groups.
Create a lesson
Related papers
Multicrossing complex of knot and secant classes
Igor Nikonov
A survey on mapping class groups of 3-manifolds
Philipp Bader, Rachael Boyd, Giulia Carfora et al.
Decompositions and diagrams of symplectic surfaces in Weinstein domains
Román Aranda, Patricia Cahn, Agniva Roy et al.
Pseudo-Anosov flow and dynamics on guts
Yu Huang
L-space surgeries on (1,1)-knots in S1× S2
Qingfeng Lyu, Zipei Nie
On the Nielsen realisation problem for cyclic groups of prime order
Christian Kremer