rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Guts of Surfaces and the Colored Jones Polynomial
  name:
    name part: Futer, David.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Kalfagianni, Efstratia.
    role:
      role term: author.
  name:
    name part: Purcell, Jessica.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2013
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: X, 170 p. 62 illus., 45 illus. in color. online resource.
  abstract: This monograph derives direct and concrete relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements. Under mild diagrammatic hypotheses, we prove that the growth of the degree of the colored Jones polynomials is a boundary slope of an essential surface in the knot complement. We show that certain coefficients of the polynomial measure how far this surface is from being a fiber for the knot; in particular, the surface is a fiber if and only if a particular coefficient vanishes. We also relate hyperbolic volume to colored Jones polynomials. Our method is to generalize the checkerboard decompositions of alternating knots. Under mild diagrammatic hypotheses, we show that these surfaces are essential, and obtain an ideal polyhedral decomposition of their complement. We use normal surface theory to relate the pieces of the JSJ decomposition of the complement to the combinatorics of certain surface spines (state graphs). Since state graphs have previously appeared in the study of Jones polynomials, our method bridges the gap between quantum and geometric knot invariants.
  table of contents: 1 Introduction -- 2 Decomposition into 3–balls -- 3 Ideal Polyhedra -- 4 I–bundles and essential product disks -- 5 Guts and fibers -- 6 Recognizing essential product disks -- 7 Diagrams without non-prime arcs -- 8 Montesinos links -- 9 Applications -- 10 Discussion and questions.
  note: by David Futer, Efstratia Kalfagianni, Jessica Purcell.
  subject:
    topic: Mathematics
  subject:
    topic: Hyperbolic geometry
  subject:
    topic: Manifolds (Mathematics)
  subject:
    topic: Complex manifolds
  subject:
    topic: Mathematics
  subject:
    topic: Manifolds and Cell Complexes (incl. Diff.Topology)
  subject:
    topic: Hyperbolic Geometry
  classification: QA613-613.8
  classification: QA613.6-613.66
  classification: 514.34
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Lecture Notes in Mathematics, 2069
  identifier: 9783642333026
  identifier: http://dx.doi.org/10.1007/978-3-642-33302-6
  record info:
    record creation date: 121227
    record change date: 20151123193237.0
    record identifier: 978-3-642-33302-6