Low dimensional homotopy groups of suspensions of the Hawaiian earring
We study the (n+1)st homotopy groups and the shape groups of the (n-1)-fold reduced and unreduced suspensions of the Hawaiian earring.
We study the (n+1)st homotopy groups and the shape groups of the (n-1)-fold reduced and unreduced suspensions of the Hawaiian earring.
We study the Lusternik-Schnirelmann category of some CW-complexes with 3 cells, built on Y = S2n Uk[i2n,i2n] e4n. In particular, we prove that an R-local space, in the sense of D. Anick, of LS-category 3 and of the homotopy type of a CW-complex with 3 R-cells, has a cup-product of length 3 in its algebra of cohomology. This result is no longer true in the framework of mild spaces.
LVM and LVMB manifolds are a large family of non kähler manifolds. For instance, Hopf manifolds and Calabi-Eckmann manifolds can be seen as LVMB manifolds. The LVM manifolds have a natural action of a real torus and the quotient of this action is a polytope. This quotient allows us to relate closely LVM manifolds to the moment-angle manifolds studied by Buchstaber and Panov. Our aim is to generalize the polytope associated to a LVM manifold to the LVMB case and study the properties of this generalization....