The quasi 𝐾𝑂-types of certain toric manifolds

On the KO-groups of toric manifolds

“…The following are equivalent: Finally, we consider the problem that how to construct toric manifolds of Mtype. Nishimura [15] gives some interesting examples, and a general idea to construct such kind of manifolds is given in [1], using the wedge construction given in [3]. Following their idea, we have the result below (see Section 4 for details).…”

“…Proposition 3.2. The filtration (15) gives a handlebody decomposition of M R . More precisely, the handlebody…”

“…, v s are all vertices of a facet F . Let M s be the handlebody in the filtration (15). Then we have a fiber bundle (16)…”

The -rings of , the Davis–Januszkiewicz spaces and certain toric manifolds

“…For toric manifolds determined by a simple polytope and a characteristic map on its facets, a description of the KO * -module structure of KO * (M 2n ) was given in [4] in terms of H * (M 2n ; Z 2 ) as a module over Sq 1 and Sq 2 . A more refined computation of the KO * -module for certain families of manifolds M 2n , is presented in [18]. The KO * -ring structure for families of toric manifolds known as Bott towers may be found in [12], without reference to KO * (DJ(K)).…”

“…. , a n ) constructed in [18] and satisfying 2 ≤ r ≤ n, a j ∈ Z and n − r odd are all Sq 2 -acyclic These varieties correspond to n-dimensional fans having n + 2 rays .…”