ON A THEOREM OF BURDE AND DE RHAM | Zendy

Daniel S. Silver | Zendy; Susan Williams | Zendy

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ON A THEOREM OF BURDE AND DE RHAM

Author(s) -

Daniel S. Silver,

Susan Williams

Publication year - 2011

Publication title -

journal of knot theory and its ramifications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.552

H-Index - 39

eISSN - 1793-6527

pISSN - 0218-2165

DOI - 10.1142/s0218216511008917

Subject(s) - mathematics , alexander polynomial , knot (papermaking) , extension (predicate logic) , group (periodic table) , knot polynomial , polynomial , pure mathematics , representation (politics) , algebra over a field , discrete mathematics , combinatorics , knot theory , knot invariant , mathematical analysis , chemistry , organic chemistry , chemical engineering , politics , computer science , law , political science , engineering , programming language

We generalize a theorem of Burde and de Rham characterizing the zeros of the Alexander polynomial. Given a representation of a knot group π, we define an extension $\tilde{\pi}$ of π, the Crowell group. For any GLNℂ representation of π, the zeros of the associated twisted Alexander polynomial correspond to representations of $\tilde{\pi}$ into the group of dilations of ℂN.

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