# Even triangulations of n–dimensional pseudo-manifolds

@article{Rubinstein2015EvenTO, title={Even triangulations of n–dimensional pseudo-manifolds}, author={J. Rubinstein and Stephan Tillmann}, journal={Algebraic \& Geometric Topology}, year={2015}, volume={15}, pages={2947-2982} }

This paper introduces even triangulations of n-dimensional pseudo-manifolds and links their combinatorics to the topology of the pseudo-manifolds. This is done via normal hypersurface theory and the study of certain symmetric representation. In dimension 3, necessary and sufficient conditions for the existence of even triangulations having one or two vertices are given. For Haken n-manifolds, an interesting connection between very short hierarchies and even triangulations is observed.

#### 7 Citations

MULTISECTIONS OF PIECEWISE LINEAR MANIFOLDS

- 2018

Recently Gay and Kirby described a new decomposition of smooth closed 4–manifolds called a trisection. This paper generalises Heegaard splittings of 3-manifolds and trisections of 4-manifolds to all… Expand

Computing trisections of 4-manifolds

- Mathematics, Medicine
- Proceedings of the National Academy of Sciences
- 2018

An algorithm to compute trisections of orientable four- manifolds using arbitrary triangulations as input results in explicit complexity bounds for the trisection genus of a 4-manifold in terms of the number of pentachora (4-simplices) in a triangulation. Expand

Trisections of 4-manifolds

- Mathematics, Medicine
- Proceedings of the National Academy of Sciences
- 2018

The gauge theory invariants are very good at distinguishing smooth 4-manifolds that are homotopy equivalent but do not help at showing that they are diffeomorphic, so what is missing is the equivalent of the higher-dimensional s-cobordism theorem, a key to the successes in higher dimensions. Expand

Multisections of piecewise linear manifolds

- Mathematics
- 2016

Recently Gay and Kirby described a new decomposition of smooth closed $4$-manifolds called a trisection. This paper generalises Heegaard splittings of $3$-manifolds and trisections of $4$-manifolds… Expand

Stable presentation length of 3-manifold groups

- Mathematics
- 2015

We introduce the stable presentation length of a finitely presented group. The stable presentation length of the fundamental group of a 3-manifold can be considered as an analogue of the simplicial… Expand

Generalized trisections in all dimensions

- Mathematics, Medicine
- Proceedings of the National Academy of Sciences
- 2018

This paper constructs multisections, which describe an n-dimensional manifold as a union of k-dimensional handlebodies, where n=2k or 2k+1, and describes a generalization of Heegaard splittings of 3-manifolds and trisection of 4- manifolds to all dimensions, using triangulations as a key tool. Expand

Simplicial moves on balanced complexes

- Mathematics
- 2015

We introduce a notion of cross-flips: local moves that transform a balanced (i.e., properly $(d+1)$-colored) triangulation of a combinatorial $d$-manifold into another balanced triangulation. These… Expand

#### References

SHOWING 1-10 OF 45 REFERENCES

Coverings and minimal triangulations of 3-manifolds

- Mathematics
- 2011

This paper uses results on the classification of minimal triangulations of 3-manifolds to produce additional results, using covering spaces. Using previous work on minimal triangulations of lens… Expand

Taut ideal triangulations of 3–manifolds

- Mathematics
- 2000

A taut ideal triangulation of a 3{manifold is a topological ideal triangulation with extra combinatorial structure: a choice of transverse orientation on each ideal 2{simplex, satisfying two simple… Expand

Branched Coverings, Triangulations, and 3-Manifolds

- Mathematics
- 2001

A canonical branched covering over each su‰ciently good simplicial complex is constructed. Its structure depends on the combinatorial type of the complex. In this way, each closed orientable… Expand

Normal surfaces in topologically finite 3-manifolds

- Mathematics
- 2004

The concept of a normal surface in a triangulated, compact 3-manifold was generalised by Thurston to a spun-normal surface in a non-compact 3-manifold with ideal triangulation. This paper defines a… Expand

ℤ2–Thurston norm and complexity of
3–manifolds, II

- Mathematics
- 2009

In this sequel to earlier papers by three of the authors, we obtain a new bound on the complexity of a closed 3--manifold, as well as a characterisation of manifolds realising our complexity bounds.… Expand

On Canonical Triangulations of Once-Punctured Torus Bundles and Two-bridge link complements

- Mathematics
- 2006

We prove the hyperbolization theorem for punctured-torus bun- dles and two-bridge links by decomposing them into ideal tetrahedra which are then given hyperbolic structures.

Trisecting 4–manifolds

- Mathematics
- 2016

We show that any smooth, closed, oriented, connected 4‐manifold can be trisected into three copies of \ k .S 1 B 3 /, intersecting pairwise in 3‐dimensional handlebodies, with triple intersection a… Expand

Homotopy Equivalences of 3-Manifolds with Boundaries

- Mathematics
- 1979

General theory.- Essential singular surfaces in some special 3-manifolds.- Characteristic submanifolds.- Singular surfaces and characteristic submanifolds.- Singular submanifolds and characteristic… Expand

Multisections of piecewise linear manifolds

- Mathematics
- 2016

Recently Gay and Kirby described a new decomposition of smooth closed $4$-manifolds called a trisection. This paper generalises Heegaard splittings of $3$-manifolds and trisections of $4$-manifolds… Expand

Growth rates, _{}-homology, and volumes of hyperbolic 3-manifolds

- Mathematics
- 1992

It is shown that if M is a closed orientable irreducible 3-manifold and n is a nonnegative integer, and if H 1 (M, Z p ) has rank ≥ n+2 for some prime p, then every n-generator subgroup of π 1 (M)… Expand