Burger–Iozzi–Wienhard inequalities for higher rank groups

E911358

inequality in geometry and topology mathematical concept result in bounded cohomology result in representation theory

The Burger–Iozzi–Wienhard inequalities for higher rank groups are a family of sharp bounds in bounded cohomology and representation theory that extend the classical Milnor–Wood inequality to representations of surface groups into higher rank Lie groups.

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Statements (42)

Predicate	Object
instanceOf	inequality in geometry and topology ⓘ mathematical concept ⓘ result in bounded cohomology ⓘ result in representation theory ⓘ
appliesTo	representations into Hermitian Lie groups ⓘ representations into higher rank Lie groups ⓘ representations of fundamental groups of closed surfaces ⓘ representations of surface groups ⓘ
concerns	bounded cohomology classes associated to Lie groups ⓘ surface group representations into semisimple Lie groups ⓘ topological invariants of flat bundles ⓘ
context	bounded cohomology of Lie groups ⓘ bounded cohomology of lattices in Lie groups ⓘ
developedBy	Alessandra Iozzi NERFINISHED ⓘ Anna Wienhard NERFINISHED ⓘ Marc Burger NERFINISHED ⓘ
extends	Milnor–Wood inequality NERFINISHED ⓘ
field	bounded cohomology ⓘ differential geometry ⓘ geometric group theory ⓘ low-dimensional topology ⓘ representation theory of Lie groups ⓘ
generalizes	Milnor–Wood inequality for flat circle bundles NERFINISHED ⓘ
givesBoundOn	Toledo invariant of a representation NERFINISHED ⓘ norm of pullback of bounded Kähler class ⓘ
hasProperty	cohomological formulation ⓘ invariant under conjugation of representations ⓘ sharp bound ⓘ
namedAfter	Alessandra Iozzi NERFINISHED ⓘ Anna Wienhard NERFINISHED ⓘ Marc Burger NERFINISHED ⓘ
relatedTo	Chern–Weil theory in bounded cohomology NERFINISHED ⓘ Toledo invariant NERFINISHED ⓘ bounded Kähler class ⓘ character varieties of surface groups ⓘ higher Teichmüller theory ⓘ maximal representations ⓘ rigidity of maximal representations into Hermitian Lie groups ⓘ symplectic geometry of representation varieties ⓘ
usedFor	characterization of maximal representations ⓘ rigidity results for surface group representations ⓘ study of deformation spaces of representations ⓘ

Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

Milnor–Wood inequality → generalizedBy → Burger–Iozzi–Wienhard inequalities for higher rank groups ⓘ