1 edition of **Guts of Surfaces and the Colored Jones Polynomial** found in the catalog.

- 293 Want to read
- 14 Currently reading

Published
**2013**
by Springer Berlin Heidelberg, Imprint: Springer in Berlin, Heidelberg
.

Written in English

- Hyperbolic Geometry,
- Mathematics,
- Cell aggregation,
- Manifolds and Cell Complexes (incl. Diff.Topology)

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.

**Edition Notes**

Statement | by David Futer, Efstratia Kalfagianni, Jessica Purcell |

Series | Lecture Notes in Mathematics -- 2069 |

Contributions | Kalfagianni, Efstratia, Purcell, Jessica, SpringerLink (Online service) |

Classifications | |
---|---|

LC Classifications | QA613-613.8, QA613.6-613.66 |

The Physical Object | |

Format | [electronic resource] / |

Pagination | X, 170 p. 62 illus., 45 illus. in color. |

Number of Pages | 170 |

ID Numbers | |

Open Library | OL27042464M |

ISBN 10 | 9783642333026 |

Find many great new & used options and get the best deals for Lecture Notes in Mathematics Ser.: Guts of Surfaces and the Colored Jones Polynomial by Efstratia Kalfagianni, David Futer and Jessica Purcell (, Trade Paperback) at the best online prices at eBay! Free shipping for many products! in the study of knot polynomial invariants (A-orB-adequacy), we derive direct and concrete relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements. We prove that the growth of the degree of the colored Jones polynomials .

Guts of surfaces and the colored Jones polynomial () Guts of surfaces and the colored Jones polynomial () Milnor fiber boundary of a non-isolated surface singularity () Complex manifolds, foliations and uniformization () Lectures on Duflo. Guts of surfaces and the colored Jones polynomial With David Futer and Efstratia Kalfagianni. Lecture Notes in Mathematics, Vol. , Springer, Berlin, Preprint version ( pages). ArXiv. Volumes of chain links With James Kaiser and Clint Rollins. Journal of Knot Theory and Its Ramifications, Vol. 21 (), No. 11, , 17 pp.

We show that the strong slope conjecture implies that the degree of the colored Jones polynomial detects all torus knots. As an application we obtain that an adequate knot that has the same colored Jones polynomial degrees as a torus knot must be a $(2,q)$-torus knot. Guts of Surfaces and the Colored Jones Polynomial, Lecture Notes in Math. Guts of surfaces and the colored Jones polynomial, with D. Futer and J. Purcell, (Research Monograph), Lecture Notes in Mathematics, Vol. , xii+ p., Berlin, Springer ().

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This monograph derives direct and concrete relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and. Buy Guts of Surfaces and the Colored Jones Polynomial (Lecture Notes in Mathematics ()) on FREE SHIPPING on qualified orders Guts of Surfaces and the Colored Jones Polynomial (Lecture Notes in Mathematics ()): Futer, David, Kalfagianni, Efstratia, Purcell, Jessica: : BooksCited by: 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. naturally in the study of knot polynomial invariants (A– or B–adequacy), we derive direct and concrete relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements.

We prove that the growth of the degree of the colored Jones polynomials is aCited by: Guts of Surfaces and the Colored Jones Polynomial. Book August Our results also yield concrete relations between hyperbolic geometry and colored Jones polynomials: for certain families.

This work 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 that arise naturally in the study of knot. Lee "Guts of Surfaces and the Colored Jones Polynomial" por David Futer disponible en Rakuten Kobo. This monograph derives direct and concrete relations between colored Jones polynomials and the topology of incompressibl Brand: Springer Berlin Heidelberg.

Guts of Surfaces and the Colored Jones Polynomial (Lecture Notes in Mathematics Book ) (English Edition) eBook: Futer, David, Kalfagianni, Efstratia, Purcell, Jessica: : Kindle Store. 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, and that certain coe cients of the polynomial measure how far this surface is from being a ber in the knot complement.

In particular, the surface is a ber if and only if a certain coe cient vanishes. Guts of Surfaces and the Colored Jones Polynomial by David Futer,Efstratia Kalfagianni,Jessica Purcell Book Resume: This monograph derives direct and concrete relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements.

/ Guts and Fibers. Guts of Surfaces and the Colored Jones Polynomial. Guts of Surfaces and the Colored Jones Polynomial. Springer-Verlag London Ltd., pp.

(Lecture Notes in. from book Guts of Surfaces and the Colored Jones Polynomial (pp) Guts of Surfaces and the Colored Jones Polynomial Discussion and Questions Article January with 29 Reads.

Book. With David Futer and Jessica S. Purcell, Kalfagianni is co-author of the research monograph Guts of Surfaces and the Colored Jones Polynomial (Lecture Notes in MathematicsSpringer, ). The monograph derives relations between colored Jones polynomials, the topology of incompressible spanning surfaces in knot and link complements.

Guts Of Surfaces And The Colored Jones Polynomial. Welcome,you are looking at books for reading, the Guts Of Surfaces And The Colored Jones Polynomial, you will able to read or download in Pdf or ePub books and notice some of author may have lock the live reading for some of ore it need a FREE signup process to obtain the book.

Guts of surfaces and the colored Jones polynomial. Guts of surfaces and the colored Jones polynomial. By David Futer, Efstratia Kalfagianni and Jessica S.

Purcell. 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 that arise.

Abstract. This work initiates a systematic study of relations between quantum and geometric knot invariants. Under mild diagrammatic hypotheses that arise naturally in the study of knot polynomial invariants (A – or B–adequacy), we derive direct and concrete relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements.

Guts of Surfaces and the Colored Jones Polynomial. Guts of Surfaces and the Chapter. First Online: 04 October Downloads; Part of the Lecture Notes in Mathematics book series (LNM Guts and Fibers. In: Guts of Surfaces and the Colored Jones Polynomial.

Lecture Notes in Mathematics, vol Springer, Berlin, Heidelberg. In Guts of Surfaces and the Colored Jones Polynomial (pp. (Lecture Notes in Mathematics; Vol. (Lecture Notes in Mathematics; Vol. Springer-Verlag London Ltd.

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 that arise naturally in the study of knot polynomial invariants (A- or B-adequacy), we prove that the growth of the degree of the colored Jones polynomials is a boundary.

As a result, geometric information about a knot complement, such as its volume, gives topological invariants of the knot. Since the mid’s, knot theory has also been invigorated by ideas from quantum physics, which have led to powerful and subtle knot invariants, including the Jones polynomial and its relatives, the colored Jones polynomials.

Guts of Surfaces and the Colored Jones Polynomial. by David Futer,Efstratia Kalfagianni,Jessica Purcell. Lecture Notes in Mathematics (Book ) Share your thoughts Complete your review. Tell readers what you thought by rating and reviewing this book.

Rate it * You Rated it *Brand: Springer Berlin Heidelberg.Efstratia Kalfagianni: free download. Ebooks library. On-line books store on Z-Library | B–OK. Download books for free.

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