# Pontryagin algebras of some moment-angle-complexes

@article{Veryovkin2015PontryaginAO, title={Pontryagin algebras of some moment-angle-complexes}, author={Yakov Veryovkin}, journal={arXiv: Algebraic Topology}, year={2015} }

We consider the problem of describing the Pontryagin algebra (loop homology) of moment-angle complexes and manifolds. The moment-angle complex Z_K is a cell complex built of products of polydiscs and tori parametrised by simplices in a finite simplicial complex K. It has a natural torus action and plays an important role in toric topology. In the case when K is a triangulation of a sphere, Z_K is a topological manifold, which has interesting geometric structures.
Generators of the Pontryagin…

## 4 Citations

Iterated Higher Whitehead Products in Topology of Moment-Angle Complexes

- MathematicsSiberian Mathematical Journal
- 2019

We give an example of a simplicial complex whose corresponding moment-angle complex is homotopy equivalent to a wedge of spheres, but there is a sphere that cannot be realized by any linear…

Polyhedral products, and relations in the commutator subgroup of a right-angled Coxeter group

- Mathematics
- 2019

We give a criterion of the existence of a presentation with a single relation for the commutator subgroup $RC_{\mathscr{K}}'$ of a right-angled Coxeter group $RC_{\mathscr{K}}$. Namely, we prove that…

Polyhedral products and commutator subgroups of right-angled Artin and Coxeter groups

- Mathematics
- 2016

We construct and study polyhedral product models for classifying spaces of right-angled Artin and Coxeter groups, general graph product groups and their commutator subgroups. By way of application,…

One-relator groups and algebras related to polyhedral products

- Mathematics
- 2020

We link distinct concepts of geometric group theory and homotopy theory through underlying combinatorics. For a flag simplicial complex $K$, we specify a necessary and sufficient combinatorial…

## References

SHOWING 1-6 OF 6 REFERENCES

Homotopy types of moment-angle complexes for flag complexes

- Mathematics
- 2012

We study the homotopy types of moment-angle complexes, or equivalently, of complements of coordinate subspace arrangements. The overall aim is to identify the simplicial complexes K for which the…

Intersections of Quadrics, Moment-angle Manifolds and Connected Sums

- Mathematics
- 2009

The topology of the intersection of two real homogeneous coaxial quadrics was studied by the second author who showed that its intersection with the unit sphere is in most cases diffeomorphic to a…

Toric Topology

- Mathematics
- 2012

Toric topology emerged in the end of the 1990s on the borders of equivariant topology, algebraic and symplectic geometry, combinatorics and commutative algebra. It has quickly grown up into a very…

Real quadrics in Cn, complex manifolds and convex polytopes

- Mathematics
- 2006

In this paper, we investigate the topology of a class of non-Kähler compact complex manifolds generalizing that of Hopf and Calabi-Eckmann manifolds. These manifolds are diffeomorphic to special…

Math

- Soc., to appear (2015); arXiv:
- 1211