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Orders that are étale-locally isomorphic

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The Holder-Poincaré duality for Lqp-cohomology

Marc Troyanov

We prove the following version of Poincaré, duality for reduced L (q,p) -cohomology: For any 1 < q, p < a, the Lqp -cohomology of a Riemannian manifold is in duality with the interior Lp'q'-cohomology for 1/p + 1/p' = 1/q + 1/q' = 1. ...

Springer Netherlands2012

Cohomology of GKM fiber bundles

Silvia Sabatini

The equivariant cohomology ring of a GKM manifold is isomorphic to the cohomology ring of its GKM graph. In this paper we explore the implications of this fact for equivariant fiber bundles for which the total space and the base space are both GKM and deri ...

Springer Verlag2012

Multiplicative structure in equivariant cohomology

Kathryn Hess Bellwald

We introduce the notion of a strongly homotopy-comultiplicative resolution of a module coalgebra over a chain Hopf algebra, which we apply to proving a comultiplicative enrichment of a well-known theorem of Moore concerning the homology of quotient spaces ...

Elsevier2012

Lattice theoretic approach to space-time codes from division algebras

Cyril Becker

This master project on algebraic coding theory gathers various techniques from lattice theory, central simple algebras and algebraic number theory. The thesis begins with the formulation of the engineering problem into mathematical form. It presents how sp ...

2012

The norm of the Euler class

Nicolas Monod

We prove that the norm of the Euler class

\mathcal{E}

for flat vector bundles is

2^{-n}

(in even dimension

n

, since it vanishes in odd dimension). This shows that the Sullivan-Smillie bound considered by Gromov and Ivanov-Turaev is sharp. We construc ...

Springer Verlag2012

Some remarks on orbit sets of unimodular rows

Jean Fasel

Let A be a d-dimensional smooth algebra over a perfect field of characteristic not 2. Let Um(n+1)(A)/En+1 (A) be the set of unimodular rows of length n + 1 up to elementary transformations. If n >= (d + 2)/2, it carries a natural structure of group as disc ...

2011

Centres of centralizers of unipotent elements in simple algebraic groups

Donna Testerman

Let G be a simple algebraic group defined over an algebraically closed field k whose characteristic is either 0 or a good prime for G, and let u is an element of G be unipotent. We study the centralizer C-G(u), especially its centre Z(C-G(u)). We calculate ...

2011

Linear Algebraic Groups and Finite Groups of Lie Type

Donna Testerman, Gunter Malle

Originating from a summer school taught by the authors, this concise treatment includes many of the main results in the area. An introductory chapter describes the fundamental results on linear algebraic groups, culminating in the classification of semisim ...

Cambridge University Press2011

Cobordism, Cohomology Theories and Formal Group Laws

Lev Kiwi

We first explore the notion of G-manifold, cobordism and then discuss the generalized Pontrjagin-Thom Theorem. We then compute the cobordism rings Ω (...) using stable homotopy theory. Secondly, we investigate the relations between cohomology theories and ...

2011

On the bounded cohomology of semi-simple groups, S-arithmetic groups and products

Nicolas Monod

We prove vanishing results for Lie groups and algebraic groups (over any local field) in bounded cohomology. The main result is a vanishing below twice the rank for semi-simple groups. Related rigidity results are established for S-arithmetic groups and gr ...

De Gruyter2010

The norm of the Euler class

Nicolas Monod

We prove that the norm of the Euler class

\mathcal{E}

for flat vector bundles is

2^{-n}

(in even dimension

n

, since it vanishes in odd dimension). This shows that the Sullivan-Smillie bound considered by Gromov and Ivanov-Turaev is sharp. We construc ...

Springer Verlag2012