A note on Dehn colorings and invariant factors

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Abstract
  • If A is an abelian group and phi is an integer, let A(phi) be the subgroup of A consisting of elements a is an element of A such that phi.a = 0. We prove that if D is a diagram of a classical link L and 0 = phi(0), phi(1,)... ,phi(n-1) are the invariant factors of an adjusted Goeritz matrix of D, then the group D-A(D) of Dehn colorings of D with values in A is isomorphic to the direct product of A and A = A(phi(0)), A(phi(1)), ... ,A(phi(n-1)). It follows that the Dehn coloring groups of L are isomorphic to those of a connected sum of torus links T-(2,T-phi 1) # ... # T-(2,T-phi n-1).
TitleA note on Dehn colorings and invariant factors
CreatorWatkins, W.
Smith, Derek Alan
Traldi, Lorenzo
PublisherJournal of Knot Theory and Its Ramifications
Academic DepartmentMathematics
DivisionNatural Sciences
OrganizationLafayette College
Date IssuedDecember 2018
Date Available2019-12-05
TypeArticle
LanguageEnglish
Keywordlink colorings
Goeritz matrix
invariant factors
Bibliographic CitationSmith, D. A., L. Traldi, and W. Watkins (2018 Dec) "A note on Dehn colorings and invariant factors." Journal of Knot Theory and Its Ramifications 27 (14): 1871003.
Standard IdentifierHandle 10385/x920fx309
DOI 10.1142/S0218216518710037
Permalinkhttp://hdl.handle.net/10385/x920fx309
Rights Statement In Copyright In Copyright
Rights HoldersWorld Scientific Publishing Company
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