This paper deals with two things. First, the cohomology of canonical extensions of real topological toric manifolds is computed when coefficient ring G is a commutative ring in which 2 is unit in G. ...Second, the author focuses on a specific canonical extensions called doublings and presents their various properties. They include existence of infinitely many real topological toric manifolds admitting complex structures, and a way to construct infinitely many real toric manifolds which have an odd torsion in their cohomology groups.Moreover, some questions about real topological toric manifolds related to Halperin＇s toral rank conjecture are presented.
Small covers over wedges of polygons CHOI, Suyoung; PARK, Hanchul
Journal of the Mathematical Society of Japan,
2019, Volume:
71, Issue:
3
Journal Article
The authors compute the（rational） Betti number of real toric varieties associated to Weyl chambers of type B, and furthermore show that their integral cohomology is p-torsion free for all odd primes ...p.
In this paper, we introduce new combinatorial invariants of any finite simple graph, which arise in toric topology. We compute the i-th (rational) Betti number of the real toric variety associated to ...a graph associahedron P_{\B(G)}. It can be calculated by a purely combinatorial method (in terms of graphs) and is denoted by a_i(G). To our surprise, for specific families of the graph G, our invariants are deeply related to well-known combinatorial sequences such as the Catalan numbers and Euler zigzag numbers.
Let
P
m
(
J
) denote a simplicial complex obtainable from consecutive wedge operations from an
m
-gon. In this paper, we completely classify toric manifolds over
P
m
(
J
) and prove that all of them ...are projective. As a consequence, we provide an infinite family of projective toric manifolds.
The authors compute the(rational) Betti number of real toric varieties associated to Weyl chambers of type B, and furthermore show that their integral cohomology is p-torsion free for all odd primes ...p.
This paper deals with two things. First, the cohomology of canonical extensions of real topological toric manifolds is computed when coefficient ring G is a commutative ring in which 2 is unit in G. ...Second, the author focuses on a specific canonical extensions called doublings and presents their various properties. They include existence of infinitely many real topological toric manifolds admitting complex structures, and a way to construct infinitely many real toric manifolds which have an odd torsion in their cohomology groups.Moreover, some questions about real topological toric manifolds related to Halperin’s toral rank conjecture are presented.
A real toric space is a topological space which admits a well-behaved \(\mathbb{Z}_2^k\)-action. Real moment-angle complexes and real toric varieties are typical examples of real toric spaces. A real ...toric space is determined by a pair of a simplicial complex \(K\) and a characteristic matrix \(\Lambda\). In this paper, we provide an explicit \(R\)-cohomology ring formula of a real toric space in terms of \(K\) and \(\Lambda\), where \(R\) is a commutative ring with unity in which \(2\) is a unit. Interestingly, it has a natural \((\mathbb{Z} \oplus \operatorname*{row} \Lambda)\)-grading. As corollaries, we compute the cohomology rings of (generalized) real Bott manifolds in terms of binary matroids, and we also provide a criterion for real toric spaces to be cohomology symplectic.
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