On null cobordism classes of quasitoric manifolds and their small covers

2020 ◽  
Vol 285 ◽  
pp. 107412
Author(s):  
Jin Hong Kim
Keyword(s):  
Quasitoric Manifolds

scholarly journals Projective bundles over toric surfaces

2016 ◽  
Vol 27 (04) ◽  
pp. 1650032 ◽  
Author(s):  
Suyoung Choi ◽  
Seonjeong Park
Keyword(s):  
Toric Variety ◽  
Cohomology Ring ◽  
Line Bundles ◽  
Projective Bundle ◽  
Cohomology Rings ◽  
Toric Surfaces ◽  
Projective Bundles ◽  
Higher Dimensional ◽  
Quasitoric Manifolds

Let [Formula: see text] be the Whitney sum of complex line bundles over a topological space [Formula: see text]. Then, the projectivization [Formula: see text] of [Formula: see text] is called a projective bundle over [Formula: see text]. If [Formula: see text] is a nonsingular complete toric variety, then so is [Formula: see text]. In this paper, we show that the cohomology ring of a nonsingular projective toric variety [Formula: see text] determines whether it admits a projective bundle structure over a nonsingular complete toric surface. In addition, we show that two [Formula: see text]-dimensional projective bundles over [Formula: see text]-dimensional quasitoric manifolds are diffeomorphic if their cohomology rings are isomorphic as graded rings. Furthermore, we study the smooth classification of higher dimensional projective bundles over [Formula: see text]-dimensional quasitoric manifolds.

scholarly journals Strong cohomological rigidity of toric varieties

2017 ◽  
Vol 147 (5) ◽  
pp. 971-992
Author(s):  
Suyoung Choi ◽  
Seonjeong Park
Keyword(s):  
Betti Number ◽  
Cohomology Ring ◽  
Toric Varieties ◽  
Ring Isomorphism ◽  
Quasitoric Manifolds ◽  
Cohomological Rigidity

Every cohomology ring isomorphism between two non-singular complete toric varieties (respectively, two quasitoric manifolds), with second Betti number 2, is realizable by a diffeomorphism (respectively, homeomorphism).

scholarly journals Semifree circle actions, Bott towers and quasitoric manifolds

2008 ◽  
Vol 199 (8) ◽  
pp. 1201-1223 ◽  
Author(s):  
M Masuda ◽  
T E Panov
Keyword(s):  
Circle Actions ◽  
Quasitoric Manifolds

scholarly journals Toric origami structures on quasitoric manifolds

2015 ◽  
Vol 288 (1) ◽  
pp. 10-28
Author(s):  
Anton A. Ayzenberg ◽  
Mikiya Masuda ◽  
Seonjeong Park ◽  
Haozhi Zeng
Keyword(s):  
Quasitoric Manifolds

scholarly journals Topological classification of quasitoric manifolds with second Betti number 2

2012 ◽  
Vol 256 (1) ◽  
pp. 19-49 ◽  
Author(s):  
Suyoung Choi ◽  
Seonjeong Park ◽  
Dong Youp Suh
Keyword(s):  
Betti Number ◽  
Topological Classification ◽  
Quasitoric Manifolds

Equivariant $$\varvec{K}$$-theory of quasitoric manifolds

2019 ◽  
Vol 129 (5) ◽  
Author(s):  
Jyoti Dasgupta ◽  
Bivas Khan ◽  
V Uma
Keyword(s):  
Quasitoric Manifolds ◽  
K Theory
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