Tunnel number and bridge number of composite genus 2 spatial graphs

Taylor, Scott A.; Tomova, Maggy

doi:10.2140/pjm.2021.314.451

Cited by 1 publication

(3 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The invariant x ω (M, T) is twice the negative of the "Heegaard number" defined by Mecchia-Zimmerman [15]. Dividing by 2 would also make the comparison with [37,38] easier. However, since orbifold Euler characteristic need not be integral, making that normalisation would unpleasantly complicate some of the calculations in this paper.…”

Section: General Notions Orbifold Sums and Orbifold Heegaard Surfacesmentioning

confidence: 99%

“…We explain this in Section 4 using orbifolds. Part of the point of this paper is to advertise the very useful properties of the invariant net x ω , which is closely related to the invariant "net extent" of [37,38].…”

Section: Introductionmentioning

confidence: 99%

“…Acknowledgments. I am grateful to Marc Lackenby for suggesting the idea to apply the techniques of [38] to orbifolds and equivariant Heegaard genus. Daryl Cooper, Yo'av Rieck, Marty Scharlemann, and an anonymous referee provided helpful comments.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Equivariant Heegaard genus of reducible 3-manifolds

Taylor¹

2023

Math. Proc. Camb. Phil. Soc.

Self Cite

View full text Add to dashboard Cite

The equivariant Heegaard genus of a 3-manifold W with the action of a finite group G of diffeomorphisms is the smallest genus of an equivariant Heegaard splitting for W. Although a Heegaard splitting of a reducible manifold is reducible and although if W is reducible, there is an equivariant essential sphere, we show that equivariant Heegaard genus may be super-additive, additive, or sub-additive under equivariant connected sum. Using a thin position theory for 3-dimensional orbifolds, we establish sharp bounds on the equivariant Heegaard genus of reducible manifolds, similar to those known for tunnel number. Along the way, we make use of a new invariant for W which is much better behaved under equivariant sums.

show abstract

Section: General Notions Orbifold Sums and Orbifold Heegaard Surfacesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%