English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT
 
 
DownloadE-Mail
  The dihedral genus of a knot

Cahn, P., & Kjuchukova, A. (2020). The dihedral genus of a knot. Algebraic & Geometric Topology, 20(4), 1939-1963. doi:10.2140/agt.2020.20.1939.

Item is

Files

show Files
hide Files
:
Cahn-Kjuchukova_The dihedral genus of a knot_2020.pdf (Publisher version), 420KB
Name:
Cahn-Kjuchukova_The dihedral genus of a knot_2020.pdf
Description:
Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer Allianz- bzw. Nationallizenz frei zugänglich. / This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence respectively.
OA-Status:
Green
Visibility:
Public
MIME-Type / Checksum:
application/pdf / [MD5]
Technical Metadata:
Copyright Date:
-
Copyright Info:
-
License:
-

Locators

show
hide
Locator:
https://doi.org/10.2140/agt.2020.20.1939 (Publisher version)
Description:
-
OA-Status:
Not specified

Creators

show
hide
 Creators:
Cahn, Patricia, Author
Kjuchukova, Alexandra1, Author           
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

Content

show
hide
Free keywords: Mathematics, Geometric Topology
 Abstract: Let $K\subset S^3$ be a Fox $p$-colored knot and assume $K$ bounds a locally
flat surface $S\subset B^4$ over which the given $p$-coloring extends. This
coloring of $S$ induces a dihedral branched cover $X\to S^4$. Its branching set
is a closed surface embedded in $S^4$ locally flatly away from one singularity
whose link is $K$. When $S$ is homotopy ribbon and $X$ a definite
four-manifold, a condition relating the signature of $X$ and the Murasugi
signature of $K$ guarantees that $S$ in fact realizes the four-genus of $K$. We
exhibit an infinite family of knots $K_m$ with this property, each with a {Fox
3-}colored surface of minimal genus $m$. As a consequence, we classify the
signatures of manifolds $X$ which arise as dihedral covers of $S^4$ in the
above sense.

Details

show
hide
Language(s): eng - English
 Dates: 2020
 Publication Status: Issued
 Pages: 26
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Degree: -

Event

show

Legal Case

show

Project information

show

Source 1

show
hide
Title: Algebraic & Geometric Topology
  Abbreviation : Algebr. Geom. Topol.
Source Genre: Journal
 Creator(s):
Affiliations:
Publ. Info: Mathematical Sciences Publishers
Pages: - Volume / Issue: 20 (4) Sequence Number: - Start / End Page: 1939 - 1963 Identifier: -