# A finite graphic calculus for 3-manifolds

@article{Benedetti1995AFG, title={A finite graphic calculus for 3-manifolds}, author={Riccardo Benedetti and Carlo Petronio}, journal={manuscripta mathematica}, year={1995}, volume={88}, pages={291-310} }

- Published 1995
DOI:10.1007/bf02567824

In this paper we provide a presentation for compact oriented 3-manifolds with non-empty boundary up to orientation-preserving homeomorphism via a calculus on suitable finite planar graphs with extra structure (decorated graphs). Closed manifolds are included in this representation by removing a 3-ball. Decorated graphs have an intrinsic geometric counterpart, as they are actually obtained by considering standard spines of the manifold and extra structure on them (decorated spines). The calculusâ€¦Â CONTINUE READING

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## EXPLOSIONS NEAR ISOLATED UNSTABLE ATTRACTORS

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## Complexity and Heegaard genus of an infinite class of compact 3-manifolds

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CITES BACKGROUND

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## Manifold Spines and Hyperbolicity Equations

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CITES METHODS & BACKGROUND

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## Three-dimensional manifolds with poor spines

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CITES BACKGROUND & METHODS

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## Traversing three-manifold triangulations and spines

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CITES BACKGROUND

## Spin structures on 3-manifolds via arbitrary triangulations

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CITES BACKGROUND

#### References

##### Publications referenced by this paper.

SHOWING 1-6 OF 6 REFERENCES

## Standard moves for standard polyhedra and spines

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Standard spines and 3-manifolds

VIEW 1 EXCERPT

## VIRO, State sum invariants of 3-manifolds and quantum 6j-symbols

VIEW 2 EXCERPTS

## MATVEEV, Universal 3-deformations of special polyhedra

VIEW 2 EXCERPTS

## SANDERSON, An introduction to piecewise linear topology

VIEW 1 EXCERPT

## A calculus forfl'amed links in S a

VIEW 1 EXCERPT