scholarly journals On the integral cohomology ring of toric orbifolds and singular toric varieties

2017 ◽  
Vol 17 (6) ◽  
pp. 3779-3810 ◽  
Author(s):  
Anthony Bahri ◽  
Soumen Sarkar ◽  
Jongbaek Song
Keyword(s):  
Cohomology Ring ◽  
Toric Varieties ◽  
Integral Cohomology

scholarly journals Infinite families of equivariantly formal toric orbifolds

2019 ◽  
Vol 31 (2) ◽  
pp. 283-301
Author(s):  
Anthony Bahri ◽  
Soumen Sarkar ◽  
Jongbaek Song
Keyword(s):  
Cohomology Ring ◽  
Toric Varieties ◽  
Simplicial Complexes ◽  
Simple Polytopes ◽  
Toric Manifolds ◽  
Integral Cohomology

AbstractThe simplicial wedge construction on simplicial complexes and simple polytopes has been used by a variety of authors to study toric and related spaces, including non-singular toric varieties, toric manifolds, intersections of quadrics and more generally, polyhedral products. In this paper we extend the analysis to include toric orbifolds. Our main results yield infinite families of toric orbifolds, derived from a given one, whose integral cohomology is free of torsion and is concentrated in even degrees, a property which might be termed integrally equivariantly formal. In all cases, it is possible to give a description of the cohomology ring and to relate it to the cohomology of the original orbifold.

On the cohomology of the sporadic simple group J4

1993 ◽  
Vol 113 (2) ◽  
pp. 253-266 ◽  
Author(s):  
David John Green
Keyword(s):  
Simple Group ◽  
Cohomology Ring ◽  
Sporadic Simple Group ◽  
Group Order ◽  
Integral Cohomology ◽  
Trivial Intersection ◽  
Extraspecial Group

In this paper we calculate part of the integral cohomology ring of the sporadic simple group J4; this group has order 221.33.5.7. 113.23.29.31.37.43. More precisely, we obtain all of the cohomology ring except for the 2-primary part. As the cohomology has already been written down [9] at the primes which divide the group order only once, we concentrate here on the primes 3 and 11. In both of these cases the Sylow p-subgroups are extraspecial of order p3 and exponent p. We use the method which identifies the p-primary cohomology with the ring of stable classes in the cohomology of a Sylow p-subgroup. The stable classes are all invariant under the action of the Sylow p-normalizer; and some time is spent finding invariant classes in the cohomology ring of , the extraspecial group. Section 2 studies the prime 11: the invariant classes are the stable classes, because the Sylow 11-subgroups have the Trivial Intersection (T.I.) property. In Section 3 we study the prime 3, and see that all conditions for invariant classes to be stable reduce to one condition.

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 The cohomology ring of certain families of periodic virtually cyclic groups

2017 ◽  
Vol 27 (07) ◽  
pp. 793-818
Author(s):  
Daciberg Lima Gonçalves ◽  
Sérgio Tadao Martins ◽  
Márcio De Jesus Soares
Keyword(s):  
Cohomology Ring ◽  
Cyclic Groups ◽  
Integral Cohomology ◽  
Farrell Cohomology

Let [Formula: see text] be a virtually cyclic of the form [Formula: see text] or [Formula: see text]. We compute the integral cohomology ring of [Formula: see text], and then obtain the periodicity of the Farrell cohomology of these groups.

scholarly journals Schubert presentation of the cohomology ring of flag manifolds

2015 ◽  
Vol 18 (1) ◽  
pp. 489-506 ◽  
Author(s):  
Haibao Duan ◽  
Xuezhi Zhao
Keyword(s):  
Lie Group ◽  
Maximal Torus ◽  
Cohomology Ring ◽  
Minimal System ◽  
Schubert Calculus ◽  
Flag Manifolds ◽  
Generators And Relations ◽  
Integral Cohomology ◽  
Minimal System Of Generators ◽  
Connected Lie Group

Let $G$ be a compact connected Lie group with a maximal torus $T$. In the context of Schubert calculus we present the integral cohomology $H^{\ast }(G/T)$ by a minimal system of generators and relations.

The integral cohomology ring of

Mathematika ◽  
1974 ◽  
Vol 21 (2) ◽  
pp. 228-232 ◽  
Author(s):  
C. B. Thomas
Keyword(s):  
Cohomology Ring ◽  
Integral Cohomology

On the integral cohomology of toric varieties

2015 ◽  
Vol 15 (02) ◽  
pp. 1650032
Author(s):  
Jin Hong Kim
Keyword(s):  
Toric Variety ◽  
Toric Varieties ◽  
Cohomology Algebra ◽  
Linear Relations ◽  
Integral Cohomology ◽  
The Ideal

It is known that the integral cohomology algebra of any smooth compact toric variety XΣ associated to a complete regular fan Σ is isomorphic to the Stanley–Reisner algebra ℤ[Σ] modulo the ideal JΣ generated by linear relations determined by Σ. The aim of this paper is to show how to determine the integral cohomology algebra of a toric variety (in particular, a projective toric variety) associated to a certain simplicial fan. As a consequence, we confirm our expectation that for a certain simplicial fan the integral cohomology algebra is also given by the same formula as in a complete regular fan.

scholarly journals The vanishing of the chow cohomology ring for affine toric varieties and additional results

2019 ◽  
Author(s):  
◽  
Ryan Matthew Richey
Keyword(s):  
Recent Work ◽  
Moduli Space ◽  
Toric Variety ◽  
Cohomology Ring ◽  
Toric Varieties ◽  
Chow Ring

From the recent work of Edidin and Satriano, given a good moduli space morphism between a smooth Artin stack and its good moduli space X, they prove that the Chow cohomology ring of X embeds into the Chow ring of the stack. In the context of toric varieties, this implies that the Chow cohomology ring of any toric variety embeds into the Chow ring of its canonical toric stack. Furthermore, the authors give a conjectural description of the image of this embedding in terms of strong cycles. One consequence of their conjectural description, and an additional conjecture, is that the Chow cohomology ring of any affine toric variety ought to vanish. We prove this result without any assumption on smoothness. Afterwards, we present a series of results related to their conjectural description, and finally, we provide a conjectural toric description of the image of this embedding for complete toric varieties by utilizing Minkowski weights.

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