Cohomology ring of the brst operator associated to the sum of two pure spinors

In the study of the Type II superstring, it is useful to consider the BRST complex associated to the sum of two pure spinors. The cohomology of this complex is an infinite-dimensional vector space. It is also a finite-dimensional algebra over the algebra of functions of a single pure spinor. In this paper we study the multiplicative structure. © 2013 World Scientific Publishing Company.

Pure Spinors in AdS and Lie Algebra Cohomology

We show that the BRST cohomology of the massless sector of the Type IIB superstring on AdS(5) x S (5) can be described as the relative cohomology of an infinite-dimensional Lie superalgebra. We explain how the vertex operators of ghost number 1, which correspond to conserved currents, are described in this language. We also give some algebraic description of the ghost number 2 vertices, which appears to be new. We use this algebraic description to clarify the structure of the zero mode sector of the ghost number two states in flat space, and initiate the study of the vertices of the higher ghost number.

Some considerations about cohomology of finite groups

In this work we present some considerations about cohomology of finite groups. In the first part we use the restriction map in cohomology to obtain some results about subgroups of finite index in a group. In the second part, we use Tate cohomology to present an application of the theory of groups with periodic cohomology in topology.

Class Notes for Math 918: Local Cohomology, Instructor Tom Marley

Topics include: Injective Module, Basic Properties of Local Cohomology Modules, Local Cohomology as a Cech Complex, Long exact sequences on Local Cohomology, Arithmetic Rank, Change of Rings Principle, Local Cohomology as a direct limit of Ext modules, Local Duality, Chevelley’s Theorem, Hartshorne- Lichtenbaum Vanishing Theorem, Falting’s Theorem.

Local cohomology with supports in the non-free locus

[EN] The groups of local cohomology with supports in the non-free locus of a module are used in order to obtain three classifications and one characterization of four classes of modules

Functional equations of polylogarithms in motivic cohomology

For an infinite field F, we study the integral relationship between the Bloch group B_2(F) and the higher Chow group CH^2(F,3) by proving some relations corresponding to the functional equations of the dilogarithm. As a second result, the groups involved in Suslin’s exact sequence 0 → Tor^1(F^× ,F^×)∼ → CH^2(F,3) → B_2(F) → 0 are identified with homology groups of the cycle complex Z^2(F,•) computing Bloch’s higher Chow groups. Using these results, we give explicit cycles in motivic cohomology generating the integral motivic cohomology groups of some specific number fields and determine whether a given cycle in the Chow group already lives in one of the other groups of Suslin’s sequence. In principle, this enables us to find a presentation of the codimension two Chow group of an arbitrary number field. Finally, we also prove some relations in the higher Chow groups of codimension three modulo 2-torsion coming from relations in the higher Bloch group B_3(F) modulo 2-torsion. Further, we can prove a series of relations in CH^ 3(Q(zeta_p),5) for a primitive pth root of unity zeta_p.

A commutative higher cycle map into Deligne-Beilinson cohomology

Das Ziel dieser Arbeit ist die Konstruktion eines Homomorphismus von partiell definierten, graduiert-kommutativen Algebren, der nach Ubergang zu rationalen Kohomologiegruppen mit der Regulatorabbildung reg zwischen motivischer und Deligne-Beilinson Kohomologie übereinstimmt.rnZu Beginn der Arbeit werden verschiedene Komplexe beschrieben, mit denen sich die motivische und die Deligne-Beilinson Kohomologie berechnen lassen.rnIm ersten Kapitel wird der Komplex der höheren Chow Ketten und der Unterkomplex der "alternierenden" Ketten "in guter Lage" eingeführt, die beide die motivische Kohomologie berechnen (letzterer mit rationalen Koeffizienten).rnIn den folgenden beiden Kapiteln werden Komplexe C_D und P_D beschrieben, mit denen sich die (rationale) Deligne-Beilinson Kohomologie berechnen lässt. Diese sind aufgebaut aus sogenannten Strömen, die im zweiten Kapitel eingeführt werden. Verknüpft sind die beiden Komplexe durch eine Auswertungsabbildung ev, die für rationale Koeffizienten zu einem Quasi-Isomorphismus wird. Auf beiden Komplexen lassen sich (Schnitt-)Produkte definieren, von denen jedoch nur das Produkt auf P_D gleichzeitig assoziativ und graduiert-kommutativ ist.rnIm vierten Kapitel wird ganz allgemein für eine Familie von Komplexen, die einer Reihe an Anforderungen genügt, ein (partiell definierter) Homomorphismus (der Regulator) von dem Komplex der höheren Chow Ketten in eben diese Komplexe konstruiert. Die beiden oben genannten Komplexe erfüllen diese Anforderungen und liefern daher Regulatoren reg_C und reg_P

On the cohomology of certain quotients of the spectrum

The aim of this note is to present a new, elementary proof of a result of Baas and Madsen on the mod p cohomology of certain quotients of the spectrum BP.

Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality

We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an essential tool. Specifically, the theory of canonical extensions implies that the (Stone-Priestley) dual spaces of MV-algebras carry the structure of topological partial commutative ordered semigroups. We use this structure to obtain two different decompositions of such spaces, one indexed over the prime MV-spectrum, the other over the maximal MV-spectrum. These decompositions yield sheaf representations of MV-algebras, using a new and purely duality-theoretic result that relates certain sheaf representations of distributive lattices to decompositions of their dual spaces. Importantly, the proofs of the MV-algebraic representation theorems that we obtain in this way are distinguished from the existing work on this topic by the following features: (1) we use only basic algebraic facts about MV-algebras; (2) we show that the two aforementioned sheaf representations are special cases of a common result, with potential for generalizations; and (3) we show that these results are strongly related to the structure of the Stone-Priestley duals of MV-algebras. In addition, using our analysis of these decompositions, we prove that MV-algebras with isomorphic underlying lattices have homeomorphic maximal MV-spectra. This result is an MV-algebraic generalization of a classical theorem by Kaplansky stating that two compact Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous [0, 1]-valued functions on the spaces are isomorphic.

A sheaf /

Much cry--little wool: On the treatment of animals. Concerning laws. On prisons and punishment. On the position of women. On social unrest. On peace--The war--And--after?--The islands of the blessed.

A sheaf from the moorland; a collection of original poems.

Mode of access: Internet.

Fresh gleanings; or, A new sheaf from the old fields of continental Europe.

Mode of access: Internet.

The last sheaf, essays

Foreword "was originally printed in the form of a letter addressed to the editor of the Times literary supplement".--p. 11.

Cohomology operations and obstructions to extending continuous functions /

"Work supported in part by U.S. Air Force Contract AF 18 (600)-1494."