Publications associées à Lie algebra cohomology

Publications associées (27)

Cochains are all you need

In this thesis, we apply cochain complexes as an algebraic model of space in a diverse range of mathematical and scientific settings. We begin with an algebraic-discrete Morse theory model of auto-encoding cochain data, connecting the homotopy theory of d ...

EPFL2024

Conditional Flatness, Fiberwise Localizations, And Admissible Reflections

Jérôme Scherer

We extend the group-theoretic notion of conditional flatness for a localization functor to any pointed category, and investigate it in the context of homological categories and of semi-abelian categories. In the presence of functorial fiberwise localizatio ...

CAMBRIDGE UNIV PRESS2023

FIBERED TORIC VARIETIES

Leonid Monin

A toric variety is called fibered if it can be represented as a total space of fibre bundle over toric base and with toric fiber. Fibered toric varieties form a special case of toric variety bundles. In this note we first give an introduction to the class ...

Independent Univ Moscow-Ium2023

The cohomology of semi-simple Lie groups, viewed from infinity

Nicolas Monod

We prove that the real cohomology of semi-simple Lie groups admits boundary values, which are measurable cocycles on the Furstenberg boundary. This generalises known invariants such as the Maslov index on Shilov boundaries, the Euler class on projective sp ...

2022

A Shadow Perspective on Equivariant Hochschild Homologies

Kathryn Hess Bellwald

Shadows for bicategories, defined by Ponto, provide a useful framework that generalizes classical and topological Hochschild homology. In this paper, we define Hochschild-type invariants for monoids in a symmetric monoidal, simplicial model category V, as ...

OXFORD UNIV PRESS2022

The algebra of Boolean matrices, correspondence functors, and simplicity

Jacques Thévenaz, Serge Bouc

We determine the dimension of every simple module for the algebra of the monoid of all relations on a finite set (i.e. Boolean matrices). This is in fact the same question as the determination of the dimension of every evaluation of a simple correspondence ...

2020

Characteristic classes as complete obstructions

Martina Rovelli

In the first part of this paper, we propose a uniform interpretation of characteristic classes as obstructions to the reduction of the structure group and to the existence of an equivariant extension of a certain homomorphism defined a priori only on a sin ...

SPRINGER HEIDELBERG2019

Simple and projective correspondence functors

Jacques Thévenaz, Serge Bouc

A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. We determine exactly which simple correspondence functors are projective. We also determine which simple ...

2021

Towards new invariants for principal bundles

Martina Rovelli

We investigate the theory of principal bundles from a homotopical point of view. In the first part of the thesis, we prove a classification of principal bundles over a fixed base space, dual to the well-known classification of bundles with a fixed structur ...

EPFL2017

A Looping-Delooping Adjunction For Topological Spaces

Martina Rovelli

Every principal G-bundle over X is classified up to equivalence by a homotopy class X -> BG, where BG is the classifying space of G. On the other hand, for every nice topological space X Milnor constructed a strict model of its loop space (Omega) over tild ...

Int Press Boston, Inc2017

Waldhausen K-theory of spaces via comodules

Kathryn Hess Bellwald

Let X be a simplicial set. We construct a novel adjunction be- tween the categories RX of retractive spaces over X and ComodX+ of X+- comodules, then apply recent work on left-induced model category structures [5], [16] to establish the existence of a left ...

Academic Press Inc Elsevier Science2016

Generalized Virasoro algebra: left-symmetry and related algebraic and hydrodynamic properties

Tudor Ratiu

Motivated by the work of Kupershmidt (J. Nonlin. Math. Phys. 6 (1998), 222 -245) we discuss the occurrence of left symmetry in a generalized Virasoro algebra. The multiplication rule is defined, which is necessary and sufficient for this algebra to be quas ...

Taylor & Francis Ltd2016

The homotopy theory of coalgebras over a comonad

Kathryn Hess Bellwald

Let K be a comonad on a model category M. We provide conditions under which the associated category of K-coalgebras admits a model category structure such that the forgetful functor to M creates both cofibrations and weak equivalences. We provide concrete ...

2014

L-2-Betti numbers and Plancherel measure

Henrik Densing Petersen

We compute L-2-Betti numbers of postliminal, locally compact, unimodular groups in terms of ordinary dimensions of reduced cohomology with coefficients in irreducible unitary representations and the Plancherel measure. This allows us to compute the L-2-Bet ...

Academic Press Inc Elsevier Science2014

Conjugation spaces and equivariant Chern classes

Jérôme Scherer

Let eta be a Real bundle, in the sense of Atiyah, over a space X. This is a complex vector bundle together with an involution which is compatible with complex conjugation. We use the fact that BU has a canonical structure of a conjugation space, as defined ...

Belgian Mathematical Soc Triomphe2013

New Techniques For Obtaining Schubert-Type Formulas For Hamiltonian Manifolds

Silvia Sabatini

In [GT], Goldin and Tolman extend some ideas from Schubert calculus to the more general setting of Hamiltonian torus actions on compact symplectic manifolds with isolated fixed points. (See also [Kn99,Kn08].) The main goal of this paper is to build on this ...

Int Press Boston, Inc2013

Spaces With Noetherian Cohomology

Jérôme Scherer

Is the cohomology of the classifying space of a p-compact group, with Noetherian twisted coefficients, a Noetherian module? In this paper we provide, over the ring of p-adic integers, such a generalization to p-compact groups of the Evens-Venkov Theorem. W ...

Cambridge University Press2013

Simple biset functors and double Burnside ring

Jacques Thévenaz, Serge Bouc

Let G be a finite group and let k be a field. Our purpose is to investigate the simple modules for the double Burnside ring kB(G,G). It turns out that they are evaluations at G of simple biset functors. For a fixed finite group H, we introduce a suitable b ...

Elsevier2013

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