• Corpus ID: 231740378

Golod and tight 3-manifolds

@inproceedings{Iriye2021GolodAT,
  title={Golod and tight 3-manifolds},
  author={Kouyemon Iriye and Daisuke Kishimoto},
  year={2021}
}
The notions Golodness and tightness for simplicial complexes come from algebra and geometry, respectively. We prove these two notions are equivalent for 3-manifold triangulations, through a topological characterization of a polyhedral product for a tightneighborly manifold triangulation of dimension ≥ 3. 
View PDF on arXiv

References

SHOWING 1-10 OF 28 REFERENCES
Golodness and polyhedral products for two-dimensional simplicial complexes
Abstract Golodness of two-dimensional simplicial complexes is studied through polyhedral products, and combinatorial and topological characterizations of Golodness of surface triangulations are…
A characterization of tightly triangulated 3-manifolds
A Golod complex with non-suspension moment-angle complex
Decompositions of polyhedral products for shifted complexes
Golodness and polyhedral products of simplicial complexes with minimal Taylor resolutions
Let K be a simplicial complex such that the Taylor resolution for its Stanley-Reisner ring is minimal. We prove that the following conditions are equivalent: (1) K is Golod; (2) any two minimal…
A Construction Principle for Tight and Minimal Triangulations of Manifolds
TLDR
A computer-friendly combinatorial scheme to obtain tight triangulations and new examples in dimensions three, four, and five are presented and shown that there are abundantly many.
On stellated spheres and a tightness criterion for combinatorial manifolds
On Stacked Triangulated Manifolds
TLDR
Two results are proved on stacked triangulated manifolds: if $\Delta$ is a tight connected closed homology $d$-manifold whosei$th homology vanishes for $1 < i < d-1$, then $\Delta $ is a stacked triangling of a manifold.
THE HOMOTOPY TYPE OF THE POLYHEDRAL PRODUCT FOR SHIFTED COMPLEXES
Minimal total absolute curvature for immersions
Immersions or maps of closed manifolds in Euclidean space, of minimal absolute total curvature are called tight in this paper. (They were called convex in [25].) After the definition in Chapter 1,…
...
1
2
3
...