Classification of trisections and the Generalized Property R Conjecture

@inproceedings{Meier2016ClassificationOT,
  title={Classification of trisections and the Generalized Property R Conjecture},
  author={Jeffrey Meier and Trent Schirmer and Alexander Martin Zupan},
  year={2016}
}
We show that the members of a large class of unbalanced four-manifold trisections are standard, and we present a family of trisections that is likely to include non-standard trisections of the four-sphere. As an application, we prove a stable version of the Generalized Property R Conjecture for $c$-component links with tunnel number at most $c$. 

Figures from this paper.

Citations

Publications citing this paper.
SHOWING 1-10 OF 27 CITATIONS

MULTISECTIONS OF PIECEWISE LINEAR MANIFOLDS

  • For Rob Kirby
  • 2018
VIEW 3 EXCERPTS
CITES RESULTS
HIGHLY INFLUENCED

Thin Position through the lens of trisections of 4-manifolds.

VIEW 6 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

Trisections of 3-manifold bundles over $S^1$

VIEW 4 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

Comparing 4–manifolds in the pants complex via trisections

VIEW 3 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

Thin Position for 4-manifolds

VIEW 5 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

Trisections and spun four-manifolds

VIEW 4 EXCERPTS
CITES BACKGROUND

Bridge trisections of knotted surfaces in $S^4$

VIEW 3 EXCERPTS
CITES METHODS & BACKGROUND

Trisections and spun 4-manifolds

VIEW 4 EXCERPTS
CITES BACKGROUND

References

Publications referenced by this paper.
SHOWING 1-10 OF 19 REFERENCES

Genus two trisections are standard

  • K. Reidemeister
  • 2014

Combinatorial methods in Dehn surgery

  • C. M. Gordon
  • In Lectures at KNOTS ’96 (Tokyo), vol. 15 of Ser. Knots Everything. World Sci. Publ., River Edge, NJ,
  • 1997
VIEW 2 EXCERPTS