The Resource Guts of Surfaces and the Colored Jones Polynomial, by David Futer, Efstratia Kalfagianni, Jessica Purcell, (electronic resource)

Guts of Surfaces and the Colored Jones Polynomial, by David Futer, Efstratia Kalfagianni, Jessica Purcell, (electronic resource)

Label
Guts of Surfaces and the Colored Jones Polynomial
Title
Guts of Surfaces and the Colored Jones Polynomial
Statement of responsibility
by David Futer, Efstratia Kalfagianni, Jessica Purcell
Creator
Contributor
Author
Author
Subject
Language
  • eng
  • eng
Summary
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
Member of
http://library.link/vocab/creatorName
Futer, David
Dewey number
514.34
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • 5aTgeP2qPtY
  • ke7blprr4Kw
  • -Zv47Ql98V8
Image bit depth
0
Language note
English
LC call number
  • QA613-613.8
  • QA613.6-613.66
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
  • Kalfagianni, Efstratia.
  • Purcell, Jessica.
Series statement
Lecture Notes in Mathematics,
Series volume
2069
http://library.link/vocab/subjectName
  • Cell aggregation
  • Manifolds and Cell Complexes (incl. Diff.Topology)
  • Hyperbolic Geometry
Label
Guts of Surfaces and the Colored Jones Polynomial, by David Futer, Efstratia Kalfagianni, Jessica Purcell, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references (p. 163-166) and index
Carrier category
online resource
Carrier category code
cr
Color
not applicable
Content category
text
Content type code
txt
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
Dimensions
unknown
Edition
1st ed. 2013.
Extent
1 online resource (X, 170 p. 62 illus., 45 illus. in color.)
File format
multiple file formats
Form of item
online
Isbn
9783642333026
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-3-642-33302-6
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000102777
  • (SSID)ssj0000831484
  • (PQKBManifestationID)11470845
  • (PQKBTitleCode)TC0000831484
  • (PQKBWorkID)10872882
  • (PQKB)10283002
  • (DE-He213)978-3-642-33302-6
  • (MiAaPQ)EBC3070786
  • (EXLCZ)993400000000102777
Label
Guts of Surfaces and the Colored Jones Polynomial, by David Futer, Efstratia Kalfagianni, Jessica Purcell, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references (p. 163-166) and index
Carrier category
online resource
Carrier category code
cr
Color
not applicable
Content category
text
Content type code
txt
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
Dimensions
unknown
Edition
1st ed. 2013.
Extent
1 online resource (X, 170 p. 62 illus., 45 illus. in color.)
File format
multiple file formats
Form of item
online
Isbn
9783642333026
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-3-642-33302-6
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000102777
  • (SSID)ssj0000831484
  • (PQKBManifestationID)11470845
  • (PQKBTitleCode)TC0000831484
  • (PQKBWorkID)10872882
  • (PQKB)10283002
  • (DE-He213)978-3-642-33302-6
  • (MiAaPQ)EBC3070786
  • (EXLCZ)993400000000102777

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