| 1. |
- Al-Shujary, Ahmed, 1980-
(författare)
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Kähler-Poisson Algebras
- 2018
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The focus of this thesis is to introduce the concept of Kähler-Poisson algebras as analogues of algebras of smooth functions on Kähler manifolds. We first give here a review of the geometry of Kähler manifolds and Lie-Rinehart algebras. After that we give the definition and basic properties of Kähler-Poisson algebras. It is then shown that the Kähler type condition has consequences that allow for an identification of geometric objects in the algebra which share several properties with their classical counterparts. Furthermore, we introduce a concept of morphism between Kähler-Poisson algebras and show its consequences. Detailed examples are provided in order to illustrate the novel concepts.
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| 2. |
- Al-Shujary, Ahmed, 1980-
(författare)
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Kähler-Poisson Algebras
- 2020
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis, we introduce Kähler-Poisson algebras and study their basic properties. The motivation comes from differential geometry, where one can show that the Riemannian geometry of an almost Kähler manifold can be formulated in terms of the Poisson algebra of smooth functions on the manifold. It turns out that one can identify an algebraic condition in the Poisson algebra (together with a metric) implying that most geometric objects can be given a purely algebraic formulation. This leads to the definition of a Kähler-Poisson algebra, which consists of a Poisson algebra and a metric fulfilling an algebraic condition. We show that every Kähler- Poisson algebra admits a unique Levi-Civita connection on its module of inner derivations and, furthermore, that the corresponding curvature operator has all the classical symmetries. Moreover, we present a construction procedure which allows one to associate a Kähler-Poisson algebra to a large class of Poisson algebras. From a more algebraic perspective, we introduce basic notions, such as morphisms and subalgebras, as well as direct sums and tensor products. Finally, we initiate a study of the moduli space of Kähler-Poisson algebras; i.e for a given Poisson algebra, one considers classes of metrics giving rise to non-isomorphic Kähler-Poisson algebras. As it turns out, even the simple case of a Poisson algebra generated by two variables gives rise to a nontrivial classification problem.
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| 3. |
- Artal, Enrique, et al.
(författare)
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Correction: Professor Maria Teresa Lozano and universal links (vol 87, pg 441, 1987)
- 2018
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Ingår i: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS. - : Springer. - 1578-7303 .- 1579-1505. ; 112:3, s. 621-621
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- Unfortunatelly an erratum appears in the foreword of this volume.We claim that one of the authors of the article On universal groups and three-manifolds, Invent. Math. 87 (1987), no. 3, 441–456 is W. Witten. The correct name of this author is Wilbur Carrington Whitten. W. C. Whitten is not the father of the fields medallist E. Witten, as we claim there.
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| 4. |
- Artal, Enrique, et al.
(författare)
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Professor Maria Teresa Lozano and universal links
- 2018
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Ingår i: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS. - : SPRINGER-VERLAG ITALIA SRL. - 1578-7303 .- 1579-1505. ; 112:3, s. 615-620
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- María Teresa, Maite, Lozano is a great person and mathematician, in these pages we can only give a very small account of her results trying to resemble her personality. We will focus our attention only on a few of the facets of her work, mainly in collaboration with Mike Hilden and José María Montesinos because as Maite Lozano pointed out in an international conference in Umeå University in June 2017, where she was a plenary speaker:I am specially proud of been part of the team Hilden-Lozano-Montesinos (H-L-M), and of our mathematical achievements
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| 5. |
- Banda, Adson, 1576-
(författare)
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Coherent functors and asymptotic properties
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis we study properties of the so called coherent functors. Coherent functors were first introduced by Auslander in 1966 in a general setting. Coherent functors have been used since then as powerful tools for different purposes: to describe infinitesimal deformation theory, to describe algebraicity of a stack or to study properties of Rees algebras.In 1998, Hartshorne proved that half exact coherent functors over a discrete valuation ring ? are direct sums of the identity functor, Hom-functors of quotient modules of ? and tensor products of quotient modules of ?. In our first article (Paper A), we obtain a similar characterization for half exact coherent functors over a much wider class of rings: Dedekind domains. This fact allows us to classify half exact coherent functors over Dedekind domains.In our second article (Paper B), coherent functors over noetherian rings are considered. We study asymptotic properties of sets of prime ideals connected with coherent functors applied to artinian modules or finitely generated modules. Also considering quotient modules M /anM, where an is the nthpower of an ideal ?, one obtains that the Betti and Bass numbers of the images under a coherent functor of the quotient modules above are polynomials in n for large n. Furthermore, the lengths of these image modules are polynomial in ?, for large ?, under the condition that the image modules have finite length.
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| 6. |
- Banda, Adson
(författare)
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Half–Exact Coherent Functors over PIDs and Dedekind Domains
- 2016
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The focus of this thesis is to characterize half–exact coherent functors over principal ideal domains (PIDs) and Dedekind domains. Ever since they where discovered, coherent functors have been useful in the study of some mathematical objects. We aim to explore a little more about them in this thesis.We first give here a review of the general categorical notions relevant to the characterization. We also review the functors Ext(M,−) and Tor(M,−) on the category on A–modules, where A is a commutative ring and M is an A–module.With the assumption that A is a commutative noetherian ring, we introduce coherent functors defined on the category of finitely generated A–modules. It is then shown in the paper that any half–exact coherent functor over a PID, and more generally over a Dedekind domain, arises from a complex of projective modules.
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| 7. |
- Bartolini, Gabriel, et al.
(författare)
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On automorphisms groups of cyclic p-gonal Riemann surfaces
- 2013
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Ingår i: Journal of symbolic computation. - : Elsevier. - 0747-7171 .- 1095-855X. ; 57, s. 61-69
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Tidskriftsartikel (refereegranskat)abstract
- In this work we obtain the group of conformal and anticonformal automorphisms of real cyclic p-gonal Riemann surfaces, where p⩾3p⩾3 is a prime integer and the genus of the surfaces is at least (p−1)2+1(p−1)2+1. We use Fuchsian and NEC groups, and cohomology of finite groups.
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| 8. |
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| 9. |
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| 10. |
- Bartolini, Gabriel, 1983-
(författare)
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On the Branch Loci of Moduli Spaces of Riemann Surfaces
- 2012
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The spaces of conformally equivalent Riemann surfaces, Mg where g ≥ 1, are not manifolds. However the spaces of the weaker Teichmüller equivalence, Tg are known to be manifolds. The Teichmüller space Tg is the universal covering of Mg and Mg is the quotient space by the action of the modular group. This gives Mg an orbifold structure with a branch locus Bg. The branch loci Bg can be identified with Riemann surfaces admitting non-trivial automorphisms for surfaces of genus g ≥ 3. In this thesis we consider the topological structure of Bg. We study the connectedness of the branch loci in general by considering families of isolated strata and we we establish that connectedness is a phenomenon for low genera. Further, we give the orbifold structure of the branch locus of surfaces of genus 4 and genus 5 in particular, by studying the equisymmetric stratification of the branch locus.Paper 1. In this paper we show that the strata corresponding to actions of order 2 and 3 belong to the same connected component for arbitrary genera. Further we show that the branch locus is connected with the exception of one isolated point for genera 5 and 6, it is connected for genus 7 and it is connected with the exception of two isolated points for genus 8.Paper 2. This paper contains a collection of results regarding components of the branch loci, some of them proved in detail in other papers. It is shown that for any integer d if p is a prime such that p > (d + 2)2, there there exist isolated strata of dimension d in the moduli space of Riemann surfaces of genus (d + 1)(p − 1)/2. It is also shown that if we consider Riemann surfaces as Klein surfaces, the branch loci are connected for every genera due to reflections.Paper 3. Here we consider surfaces of genus 4 and 5. Here we study the automorphism groups of Riemann surfaces of genus 4 and 5 up to topological equivalence and determine the complete structure of the equisymmetric stratification of the branch locus.Paper 4. In this paper we establish that the connectedness of the branch loci is a phenomenon for low genera. More precisely we prove that the only genera g where Bg is connected are g = 3, 4, 13, 17, 19, 59.
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