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Satellites of Legendrian knots and representations of the Chekanov-Eliashberg Algebra

Publication ,  Journal Article
Ng, L; Rutherford, D
Published in: Algebraic and Geometric Topology
August 1, 2013

We develop a close relation between satellites of Legendrian knots in ℝ3 and the Chekanov-Eliashberg differential graded algebra of the knot. In particular, we generalize the well-known correspondence between rulings of a Legendrian knot in ℝ3 and augmentations of its DGA by showing that the DGA has finite-dimensional representations if and only if there exist certain rulings of satellites of the knot. We derive several consequences of this result, notably that the question of existence of ungraded finite-dimensional representations for the DGA of a Legendrian knot depends only on the topological type and Thurston-Bennequin number of the knot.

Duke Scholars

Published In

Algebraic and Geometric Topology

DOI

EISSN

1472-2739

ISSN

1472-2747

Publication Date

August 1, 2013

Volume

13

Issue

5

Start / End Page

3047 / 3097

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics
 

Citation

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ICMJE
MLA
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Ng, L., & Rutherford, D. (2013). Satellites of Legendrian knots and representations of the Chekanov-Eliashberg Algebra. Algebraic and Geometric Topology, 13(5), 3047–3097. https://doi.org/10.2140/agt.2013.13.3047
Ng, L., and D. Rutherford. “Satellites of Legendrian knots and representations of the Chekanov-Eliashberg Algebra.” Algebraic and Geometric Topology 13, no. 5 (August 1, 2013): 3047–97. https://doi.org/10.2140/agt.2013.13.3047.
Ng L, Rutherford D. Satellites of Legendrian knots and representations of the Chekanov-Eliashberg Algebra. Algebraic and Geometric Topology. 2013 Aug 1;13(5):3047–97.
Ng, L., and D. Rutherford. “Satellites of Legendrian knots and representations of the Chekanov-Eliashberg Algebra.” Algebraic and Geometric Topology, vol. 13, no. 5, Aug. 2013, pp. 3047–97. Scopus, doi:10.2140/agt.2013.13.3047.
Ng L, Rutherford D. Satellites of Legendrian knots and representations of the Chekanov-Eliashberg Algebra. Algebraic and Geometric Topology. 2013 Aug 1;13(5):3047–3097.

Published In

Algebraic and Geometric Topology

DOI

EISSN

1472-2739

ISSN

1472-2747

Publication Date

August 1, 2013

Volume

13

Issue

5

Start / End Page

3047 / 3097

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics