Immersions and embeddings of quasitoric manifolds over the cube

Djordje Baralic

doi:10.2298/pim1409063b

Immersions and embeddings of quasitoric manifolds over the cube

Publications de l Institut Mathematique ◽

10.2298/pim1409063b ◽

2014 ◽

Vol 95 (109) ◽

pp. 63-71 ◽

Cited By ~ 4

Author(s):

Djordje Baralic

Keyword(s):

Quasitoric Manifolds ◽

Quasitoric Manifold

A quasitoric manifold M2n over the cube In is studied. The Stiefel-Whitney classes are calculated and used as the obstructions for immersions, embeddings and totally skew embeddings. The manifold M2n, when n is a power of 2, has interesting properties: imm(M2n) = 4n ? 2, em(M2n) = 4n ? 1 and N(M2n)? 8n?3.

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Topological rigidity of quasitoric manifolds

MATHEMATICA SCANDINAVICA ◽

10.7146/math.scand.a-97303 ◽

2018 ◽

Vol 122 (2) ◽

pp. 179

Author(s):

Vassilis Metaftsis ◽

Stratos Prassidis

Keyword(s):

Homotopy Equivalent ◽

Quasitoric Manifolds ◽

Quasitoric Manifold ◽

Manifolds With Corners ◽

Standard Action

Quasitoric manifolds are manifolds that admit an action of the torus that is locally the same as the standard action of $T^n$ on $\mathbb{C}^n$. It is known that the quotients of such actions are nice manifolds with corners. We prove that a class of locally standard manifolds, that contains the quasitoric manifolds, is equivariantly rigid, i.e., that any manifold that is $T^n$-homotopy equivalent to a quasitoric manifold is $T^n$-homeomorphic to it.

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Certain generalized higher derived functors associated to quasitoric manifolds

Journal of Homotopy and Related Structures ◽

10.1007/s40062-017-0186-y ◽

2017 ◽

Vol 13 (2) ◽

pp. 395-421

Author(s):

José La Luz ◽

David Allen

Keyword(s):

Derived Functors ◽

Quasitoric Manifolds

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The higher derived functors of the primitive element functor of quasitoric manifolds

Topology and its Applications ◽

10.1016/j.topol.2011.06.054 ◽

2011 ◽

Vol 158 (16) ◽

pp. 2103-2110 ◽

Cited By ~ 2

Author(s):

David Allen ◽

Jose La Luz

Keyword(s):

Primitive Element ◽

Derived Functors ◽

Quasitoric Manifolds

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Example of C-rigid polytopes which are not B-rigid

Mathematica Slovaca ◽

10.1515/ms-2017-0236 ◽

2019 ◽

Vol 69 (2) ◽

pp. 437-448

Author(s):

Suyoung Choi ◽

Kyoungsuk Park

Keyword(s):

Cohomology Ring ◽

Combinatorial Structure ◽

Simple Polytope ◽

Quasitoric Manifold

Abstract A simple polytope P is said to be B-rigid if its combinatorial structure is characterized by its Tor-algebra, and is said to be C-rigid if its combinatorial structure is characterized by the cohomology ring of a quasitoric manifold over P. It is known that a B-rigid simple polytope is C-rigid. In this paper, we show that the B-rigidity is not equivalent to the C-rigidity.

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Projective bundles over toric surfaces

International Journal of Mathematics ◽

10.1142/s0129167x16500324 ◽

2016 ◽

Vol 27 (04) ◽

pp. 1650032 ◽

Cited By ~ 2

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.

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Strong cohomological rigidity of toric varieties

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210516000457 ◽

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).

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