• Corpus ID: 119674347

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}
}
  • Yakov Veryovkin
  • Published 1 December 2015
  • Mathematics
  • arXiv: Algebraic Topology
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… 

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References

SHOWING 1-6 OF 6 REFERENCES
Homotopy types of moment-angle complexes for flag complexes
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
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
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
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