I. M. I. Riera

activity

19992025

most citedThe Hitchin-Kobayashi correspondence, Higgs pairs and surface group representations

73 citations · 308 across the 22 of their papers we have counts for

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Showing math.DGShow all

12 papers · 1 filter

math.DG2022★ 3 cited

Non-connected Lie groups, twisted equivariant bundles and coverings

G. Barajas, O. García-Prada, P. B. Gothen +1

Let $Γ$ be a finite group acting on a Lie group $G$ . We consider a class of group extensions $1 \to G \to G^\to Γ \to 1$ defined by this action and a $2$ -cocycle of $Γ$ with v…

math.DG2019

Which finite groups act smoothly on a given $4$ -manifold?

Ignasi Mundet i Riera, Carles Sáez-Calvo

We prove that for any closed smooth $4$ -manifold $X$ there exists a constant $C$ with the property that each finite subgroup $G < D i f f (X)$ has a subgroup $N$ which is abelian or nilp…

math.DG2018

Almost fixed points of finite group actions on manifolds without odd cohomology

Ignasi Mundet i Riera

If $X$ is a smooth manifold and $G$ is a subgroup of $D i f f (X)$ we say that $(X, G)$ has the almost fixed point property if there exists a number $C$ such tha…

math.DG2017★ 1 cited

Nontrivial bundles of coadjoint orbits over $S^{2}$

David Martínez Torres, Ignasi Mundet i Riera

Let $G$ be a compact connected semisimple Lie group with Lie algebra $g$ . Let $O \subset g^{*}$ be a coadjoint orbit. The action of $G$ on $O$ …

math.DG2017

Automorphisms of generic gradient vector fields with prescribed finite symmetries

Ignasi Mundet i Riera

Let $M$ be a compact and connected smooth manifold endowed with a smooth action of a finite group $Γ$ , and let $f$ be a $Γ$ -invariant Morse function on $M$ . We prove that the space…

math.DG2015

Parabolic Higgs bundles and representations of the fundamental group of a punctured surface into a real group

Olivier Biquard, Oscar Garcia-Prada, Ignasi Mundet i Riera

We study parabolic G-Higgs bundles over a compact Riemann surface with fixed punctures, when G is a real reductive Lie group, and establish a correspondence between these objects a…

math.DG2014★ 39 cited

Finite group actions on homology spheres and manifolds with nonzero Euler characteristic

Ignasi Mundet i Riera

Let $X$ be a smooth manifold belonging to one of these three collections: acyclic manifolds (compact or not, possibly with boundary), compact connected manifolds (possibly with bou…

math.DG2013★ 6 cited

Finite group actions on 4-manifolds with nonzero Euler characteristic

Ignasi Mundet i Riera

We prove that if $X$ is a compact, oriented, connected $4$ -dimensional smooth manifold, possibly with boundary, satisfying $χ (X) \neq = 0$ , then there exists an integer $C \geq 1$ such…

math.DG2013★ 18 cited

Finite group actions on manifolds without odd cohomology

Ignasi Mundet i Riera

Let $X$ be a compact smooth manifold, possibly with boundary. Denote by $X_{1}, \dots, X_{r}$ the connected components of $X$ . Assume that the integral cohomology of $X$ is torsion free…

math.DG2009★ 73 cited

The Hitchin-Kobayashi correspondence, Higgs pairs and surface group representations

Oscar Garcia-Prada, Peter B. Gothen, Ignasi Mundet i Riera

We develop a complete Hitchin-Kobayashi correspondence for twisted pairs on a compact Riemann surface X. The main novelty lies in a careful study of the the notion of polystability…

math.DG2000

Lifts of smooth group actions to line bundles

Ignasi Mundet i Riera

Let X be a compact manifold with a smooth action of a compact connected Lie group G. Let $L \to X$ be a complex line bundle. Using the Cartan complex for equivariant cohomology, we…

math.DG1999★ 35 cited

A Hitchin-Kobayashi correspondence for Kaehler fibrations

Ignasi Mundet i Riera

Let $X$ be a compact Kaehler manifold and $E \to X$ a principal $K$ bundle, where $K$ is a compact connected Lie group. Let $A^{1, 1}$ be the set of connections on $E$ whose c…

Non-connected Lie groups, twisted equivariant bundles and coverings

Which finite groups act smoothly on a given 4-manifold?

Almost fixed points of finite group actions on manifolds without odd cohomology

Nontrivial bundles of coadjoint orbits over S2

Automorphisms of generic gradient vector fields with prescribed finite symmetries

Parabolic Higgs bundles and representations of the fundamental group of a punctured surface into a real group

Finite group actions on homology spheres and manifolds with nonzero Euler characteristic

Finite group actions on 4-manifolds with nonzero Euler characteristic

Finite group actions on manifolds without odd cohomology

The Hitchin-Kobayashi correspondence, Higgs pairs and surface group representations

Lifts of smooth group actions to line bundles

A Hitchin-Kobayashi correspondence for Kaehler fibrations

Which finite groups act smoothly on a given $4$ -manifold?

Nontrivial bundles of coadjoint orbits over $S^{2}$