Knotted surfaces with simply-connected complements
arXiv:2607.15165
summary
The paper investigates compact, oriented surfaces with a given knot as boundary that sit inside simply‑connected 4‑manifolds, showing that homologous surfaces with trivial complement fundamental group are topologically isotopic relative to their boundary.
Abstract
We study locally flat, compact, oriented, genus g, surfaces with boundary a fixed knot K, properly embedded in simply-connected 4-manifolds with boundary the 3-sphere, and whose complements have trivial fundamental group. We show that if two such surfaces are homologous then they are topologically ambiently isotopic rel. boundary.
19 pages
Topics & keywords
#knotted surfaces#4-manifolds#simply-connected complements#ambient isotopy#homology#locally flat embeddingssimply-connected complementtopological ambient isotopygenus‑g surfaceboundary knotfundamental grouphomologous surfaces