The classification of weighted projective spaces

Bahri, Abbas; Franz, Matthias; Notbohm, Dietrich; Ray, Nigel

doi:10.4064/fm220-3-3

Cited by 12 publications

(13 citation statements)

References 6 publications

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“…By [3,Equation 1.2], composing the maps z 1 → z n 1 and z 3 → z m 3 induces a homeomorphism between P(m, mn, n) and the standard projective space P(1, 1, 1) = P 2 . Using this homeomorphism, we have χ P(m, mn, n) = χ(P 2 ) = 3.…”

Section: Functional Equations For Quotient Orbifold Wreath Symmetric mentioning

confidence: 99%

Functional equations for orbifold wreath products

Farsi

Seaton

2017

Journal of Geometry and Physics

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We present generating functions for extensions of multiplicative invariants of wreath symmetric products of orbifolds presented as the quotient by the locally free action of a compact, connected Lie group in terms of orbifold sector decompositions. Particularly interesting instances of these product formulas occur for the Euler and Euler-Satake characteristics, which we compute for a class of weighted projective spaces. This generalizes results known for global quotients by finite groups to all closed, effective orbifolds. We also describe a combinatorial approach to extensions of multiplicative invariants using decomposable functors that recovers the formula for the Euler-Satake characteristic of a wreath product of a global quotient orbifold.2010 Mathematics Subject Classification. Primary 57S15, 55S15; Secondary 55N91, 05A15.

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Section: Functional Equations For Quotient Orbifold Wreath Symmetric mentioning

confidence: 99%

Functional equations for orbifold wreath products

Farsi

Seaton

2017

Journal of Geometry and Physics

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“…As quotient spaces they have a natural orbifold structure and include, in complex dimension 1, the orbifolds named teardrops by Thurston in [17]. We start by recalling some basic facts about their classification as done in [4].…”

Section: Weighted Projective Spacesmentioning

confidence: 99%

“…It is known that two weighted projective spaces are isomorphic as projective varieties if and only if they are homeomorphic [4]. Moreover, every isomorphism class can be represented by a normalized weight, and two such spaces are isomorphic if and only if they have the same normalized weights, up to order.…”

Section: Weighted Projective Spacesmentioning

confidence: 99%

“…Classically, two (coprime) weight vectors correspond to isomorphic weighted projective spaces if and only if one can be obtained from the other with an iterated application (in any order) of admissible multiplications and divisions [4]. So for example, one has P(1, 2, 2) ≃ P(2, 3, 6) ≃ CP 2 while P(1, 1, 2) ≃ CP 2 (in particular, D 0 (2) is admissible in the former case, while M 2 (2) is not admissible in the latter case).…”

Section: The Left Inverse Ofmentioning

confidence: 99%

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Quantum Weighted Projective and Lens Spaces

D’Andrea

Landi

2015

Commun. Math. Phys.

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Abstract. We generalize to quantum weighted projective spaces in any dimension previous results of us on K-theory and K-homology of quantum projective spaces 'tout court'. For a class of such spaces, we explicitly construct families of Fredholm modules, both bounded and unbounded (that is spectral triples), and prove that they are linearly independent in the K-homology of the corresponding C * -algebra. We also show that the quantum weighted projective spaces are base spaces of quantum principal circle bundles whose total spaces are quantum lens spaces. We construct finitely generated projective modules associated with the principal bundles and pair them with the Fredholm modules, thus proving their non-triviality.Dedicated to Marc Rieffel on the occasion of his 75th birthday

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“…Therefore, toric orbifolds do not satisfy cohomological rigidity. However, in the above counter-examples, two weighted projective spaces with isomorphic cohomology rings are homotopy equivalent [BFNR13]. Hence we take a step back and ask a homotopical version of the cohomogical rigidity: their homotopy theory.…”

Section: Introductionmentioning

confidence: 99%

The homotopy classification of four-dimensional toric orbifolds

Fu,

So,

Song

2020

Preprint

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Let X be a 4-dimensional toric orbifold. If H 3 (X) has a non-trivial odd primary torsion, then we show that X is homotopy equivalent to the wedge of a Moore space and a CW-complex. As a corollary, given two 4-dimensional toric orbifolds having no 2-torsion in the cohomology, we prove that they have the same homotopy type if and only their integral cohomology rings are isomorphic.Question 1.1. Are two toric orbifolds homotopy equivalent if their integral cohomology rings are isomorphic as graded rings?This paper aims to answer this question for certain 4-dimensional toric orbifolds. We first study certain CW-complexes which model 4-dimensional toric orbifolds and investigate

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The classification of weighted projective spaces

Cited by 12 publications

References 6 publications

Functional equations for orbifold wreath products

Functional equations for orbifold wreath products

Quantum Weighted Projective and Lens Spaces

The homotopy classification of four-dimensional toric orbifolds

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