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Branched Standard Spines of 3-manifolds

  • Book
  • © 1997

Overview

Authors:
  1. Riccardo Benedetti
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  2. Carlo Petronio
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1653)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. Motivations, plan and statements

    • Riccardo Benedetti, Carlo Petronio
    Pages 1-12

  3. A review on standard spines and o-graphs

    • Riccardo Benedetti, Carlo Petronio
    Pages 13-22

  4. Branched standard spines

    • Riccardo Benedetti, Carlo Petronio
    Pages 23-39

  5. Manifolds with boundary

    • Riccardo Benedetti, Carlo Petronio
    Pages 40-63

  6. Combed closed manifolds

    • Riccardo Benedetti, Carlo Petronio
    Pages 64-72

  7. More on combings, and the closed calculus

    • Riccardo Benedetti, Carlo Petronio
    Pages 73-84

  8. Framed and spin manifolds

    • Riccardo Benedetti, Carlo Petronio
    Pages 85-97

  9. Branched spines and quantum invariants

    • Riccardo Benedetti, Carlo Petronio
    Pages 98-107

  10. Problems and perspectives

    • Riccardo Benedetti, Carlo Petronio
    Pages 108-120

  11. Homology and cohomology computations

    • Riccardo Benedetti, Carlo Petronio
    Pages 121-126

  12. Back Matter

    Pages 127-132
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Keywords

About this book

This book provides a unified combinatorial realization of the categroies of (closed, oriented) 3-manifolds, combed 3-manifolds, framed 3-manifolds and spin 3-manifolds. In all four cases the objects of the realization are finite enhanced graphs, and only finitely many local moves have to be taken into account. These realizations are based on the notion of branched standard spine, introduced in the book as a combination of the notion of branched surface with that of standard spine. The book is intended for readers interested in low-dimensional topology, and some familiarity with the basics is assumed. A list of questions, some of which concerning relations with the theory of quantum invariants, is enclosed.

Bibliographic Information

  • Book Title: Branched Standard Spines of 3-manifolds

  • Authors: Riccardo Benedetti, Carlo Petronio

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0093620

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1997

  • Softcover ISBN: 978-3-540-62627-5Published: 20 March 1997

  • eBook ISBN: 978-3-540-68345-2Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 140

  • Topics: Manifolds and Cell Complexes (incl. Diff.Topology)

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