The number of small covers over cubes and the product of at most three simplices up to equivariant cobordism

Chen, Yanchang; Wang, Yanying

doi:10.3792/pjaa.87.95

Cited by 3 publications

(6 citation statements)

References 6 publications

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“…Also using similar techniques Lü extends this result to small covers over P n × ∆ 1 where P n is a product of simplices (see [15,Theorem 3.4]). From [15] we came to know that Cheng and Wang [1] and Lü and Tan [16] have proved that any real Bott manifold bounds equivariantly using different methods. However our Corollary 5.7 regarding oriented cobordism is new and could not be explicitly found in the papers [1,16,15] comments and suggestions and Prof. M. Masuda for his valuable comments and suggestions on earlier versions of the manuscript.…”

Section: Spin Structure On Real Bott Manifoldsmentioning

confidence: 99%

“…From [15] we came to know that Cheng and Wang [1] and Lü and Tan [16] have proved that any real Bott manifold bounds equivariantly using different methods. However our Corollary 5.7 regarding oriented cobordism is new and could not be explicitly found in the papers [1,16,15] comments and suggestions and Prof. M. Masuda for his valuable comments and suggestions on earlier versions of the manuscript. I finally thank University Grants Commission (UGC), India for financial assistance.…”

Section: Spin Structure On Real Bott Manifoldsmentioning

confidence: 99%

“…A Bott tower is an iterated sequence of fibre bundles with fibre at each stage being CP 1 . The manifold at each stage of the sequence is called a Bott manifold.…”

Section: Introductionmentioning

confidence: 99%

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On the Topology of Real Bott Manifolds

Dsouza

2018

Indian J Pure Appl Math

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Generalized Bott manifolds (over C and R) have been defined by Choi, Masuda and Suh in [4]. In this article we extend the results of [7] on the topology of real Bott manifolds to generalized real Bott manifolds. We give a presentation of the fundamental group, prove that it is solvable and give a characterization for it to be abelian.We further prove that these manifolds are aspherical only in the case of real Bott manifolds and compute the higher homotopy groups. Furthermore, using the presentation of the cohomology ring with Z 2 -coefficients, we derive a combinatorial characterization for orientablity and spin structure.

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Section: Spin Structure On Real Bott Manifoldsmentioning

confidence: 99%

Section: Spin Structure On Real Bott Manifoldsmentioning

confidence: 99%

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On the Topology of Real Bott Manifolds

Dsouza

2018

Indian J Pure Appl Math

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“…When 1 = n 2 = n 3 , ∆ 1 × ∆ n 2 × ∆ n 3 is a 3-cube I 3 and the automorphism group Aut(F (I 3 )) S 3 2 × S 3 . From [4], we know that there are 259 equivariant homeomorphism classes of small covers over I 3 .…”

Section: Theorem 41 the Number Of Equivariant Homeomorphism Classesmentioning

confidence: 99%

“…Products of simplices are an interesting class of polytopes and more complicated than one might think [13]. And small covers over products of simplices have become an important search object [3,4,5,6,8,10]. Motivated by these, we determine the number of equivariant homeomorphism classes of small covers over a product of m simplices for m ≤ 3 or for the dimension of each simplex being greater than 1 and m > 3 (see Theorem 2.7 and Theorems 4.1-4.2).…”

Section: Introductionmentioning

confidence: 99%

Small covers over a product of simplices

Chen

Wang

2013

Filomat

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On cobordism of generalized (real) Bott manifolds

2017

Preprint

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We show that all generalized (real) Bott manifolds which are (small covers) quasitoric manifolds over a product of simplices ∆ n1 × • • • × ∆ nr × ∆ 1 are always boundaries of some manifolds. But these manifolds with the natural (Z 2 ) n action do not necessarily bound equvariantly. In addition, we can construct some examples of null-cobordant but not orientedly nullcobordant manifolds among quasitoric manifolds.2 is a simple convex polytope P n . A quasitoric manifold means a smooth orientable

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The number of small covers over cubes and the product of at most three simplices up to equivariant cobordism

Cited by 3 publications

References 6 publications

On the Topology of Real Bott Manifolds

On the Topology of Real Bott Manifolds

Small covers over a product of simplices

On cobordism of generalized (real) Bott manifolds

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