18 citations · 50 across the 28 of their papers we have counts for
12 papers · 1 filter
Counter-Examples to a generalised Toral Rank Conjecture
Manuel Amann
The toral rank conjecture speculates that the sum of the Betti numbers of a compact manifold admitting a free action of a torus of rank is bounded from below by . Clearly,…
The Omnibus Conjecture---disproved
Manuel Amann
We provide various counter-examples to the long-standing so-called "Omnibus Conjecture" in Rational Homotopy Theory. That is, we show that a space with finite dimensional even-degr…
Homology versus homotopy in fibrations and in limits
Manuel Amann
Motivated by prominent problems like the Hilali conjecture Yamaguchi--Yokura recently proposed certain estimates on the relations of the dimensions of rational homotopy and rationa…
Equivariant formality of the isotropy action on -symmetric spaces
Manuel Amann, Andreas Kollross
Compact symmetric spaces are probably one of the most prominent class of formal spaces, i.e. of spaces where the rational homotopy type is a formal consequence of the rational coho…
The Toral Rank Conjecture and variants of equivariant formality
Manuel Amann, Leopold Zoller
An action of a compact Lie group is called equivariantly formal, if the Leray--Serre spectral sequence of its Borel fibration degenerates at the E_2-term. This term is as prominent…
Deciding almost freeness of an action is NP-hard
Manuel Amann
We encode a compact Lie group action on a compact manifold by the Sullivan model of its Borel construction. We then prove that deciding whether this action is almost free is NP-har…