Hereditary properties of co-Kähler manifolds

Bazzoni, Giovanni; Lupton, Gregory; Oprea, John

doi:10.1016/j.difgeo.2016.11.002

Cited by 6 publications

(7 citation statements)

References 24 publications

(37 reference statements)

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“…In the formal case this conjecture holds, and leads to the following result (see also [, § 2.2]). Proposition Suppose

normalΦ

is a finite group acting simplicially on a formal simplicial complex

Y

with finite Betti numbers.…”

Section: Algebraic Models and Finiteness Obstructionsmentioning

confidence: 84%

Infinitesimal finiteness obstructions

Papadima

Suciu

2018

J. London Math. Soc.

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Does a space enjoying good finiteness properties admit an algebraic model with commensurable finiteness properties? In this note, we provide a rational homotopy obstruction for this to happen. As an application, we show that the maximal metabelian quotient of a very large, finitely generated group is not finitely presented. Using the theory of 1‐minimal models, we also show that a finitely generated group π admits a connected 1‐model with finite‐dimensional degree 1 piece if and only if the Malcev Lie algebra m(π) is the lower central series completion of a finitely presented Lie algebra.

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“…In the formal case this conjecture holds, and leads to the following result (see also [, § 2.2]). Proposition Suppose

normalΦ

is a finite group acting simplicially on a formal simplicial complex

Y

with finite Betti numbers.…”

Section: Algebraic Models and Finiteness Obstructionsmentioning

confidence: 84%

Infinitesimal finiteness obstructions

Papadima

Suciu

2018

J. London Math. Soc.

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“…In [3] we overlooked this simple approach and appealed rather to the techniques of Conner -Raymond and Sadowski since our main goal was to investigate the rational-homotopic properties of compact coKähler manifolds. Among the outcomes of this research, we quote the proof of the toral rank conjecture for compact coKähler manifolds (see [2]). Corollary 3.3.…”

Section: Resultsmentioning

confidence: 99%

A splitting theorem for compact Vaisman manifolds

Bazzoni¹,

Marrero²,

Oprea³

2015

Preprint

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“…It is however a little more general as it holds e.g. for any space with cohomology concentrated in even degrees and is stable under products ( [7,Prop. 3.5]).…”

Section: Corollary 511 ([34]mentioning

confidence: 99%

The Toral Rank Conjecture and variants of equivariant formality

Amann¹,

Zoller²

2019

Preprint

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An action of a compact Lie group is called equivariantly formal, if the Leray-Serre spectral sequence of its Borel fibration degenerates at the E2-term. This term is as prominent as it is restrictive.In this article, also motivated by the lack of junction between the notion of equivariant formality and the concept of formality of spaces (surging from rational homotopy theory) we suggest two new variations of equivariant formality: "MOD-formal actions" and "actions of formal core".We investigate and characterize these new terms in many different ways involving various tools from rational homotopy theory, Hirsch-Brown models, A∞-algebras, etc., and, in particular, we provide different applications ranging from actions on symplectic manifolds and rationally elliptic spaces to manifolds of non-negative sectional curvature.A major motivation for the new definitions was that an almost free action of a torus T n X possessing any of the two new properties satisfies the toral rank conjecture, i.e. dim H * (X; Q) ≥ 2 n . This generalizes and proves the toral rank conjecture for actions with formal orbit spaces.

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Hereditary properties of co-Kähler manifolds

Cited by 6 publications

References 24 publications

Infinitesimal finiteness obstructions

Infinitesimal finiteness obstructions

A splitting theorem for compact Vaisman manifolds

The Toral Rank Conjecture and variants of equivariant formality

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