On the minimal sum of Betti numbers of an almost complex manifold

  title={On the minimal sum of Betti numbers of an almost complex manifold},
  author={Michael J. Albanese and Aleksandar Milivojevic},
  journal={Differential Geometry and its Applications},

Figures from this paper

Almost complex manifolds with total Betti number three
We show the minimal total Betti number of a closed almost complex manifold of dimension 2n ≥ 8 is four, thus confirming a conjecture of Sullivan except for dimension 6. Along the way, we prove the
On the characterization of rational homotopy types and Chern classes of closed almost complex manifolds
Abstract We give an exposition of Sullivan’s theorem on realizing rational homotopy types by closed smooth manifolds, including a discussion of the necessary rational homotopy and surgery theory,
On the realization of symplectic algebras and rational homotopy types by closed symplectic manifolds
We answer a question of Oprea-Tralle on the realizability of symplectic algebras by symplectic manifolds in dimensions divisible by four, along with a question of Lupton-Oprea in all even dimensions.
Almost complex manifold with Betti number $b_i=0$ except $i=0, n/2, n$
. This paper studies existence of n = 4 k ( k > 1) dimensional simply-connected closed almost complex manifold with Betti number b i = 0 except i = 0 , n/ 2 , n . We characterize all the rational


Obstruction formulas and almost-complex manifolds
This paper contains three theorems about almost-complex manifolds. The first theorem states that, under certain conditions, the Euler characteristic of an almost-complex manifold M2n must be
Rational analogs of projective planes
In this paper, we study the existence of high-dimensional, closed, smooth manifolds whose rational homotopy type resembles that of a projective plane. Applying rational surgery, the problem can be
Obstructions to the existence of almost complex structures
1. Definitions and notation. Let M be an orientable, differentiate manifold of dimension In and let £ = (E^ M, R, x) denote the tangent bundle of M ; we assume the structural group of £ has been
On dimensions supporting a rational projective plane
A rational projective plane ([Formula: see text]) is a simply connected, smooth, closed manifold [Formula: see text] such that [Formula: see text]. An open problem is to classify the dimensions at
Hirzebruch L-polynomials and multiple zeta values
We express the coefficients of the Hirzebruch L-polynomials in terms of certain alternating multiple zeta values. In particular, we show that every monomial in the Pontryagin classes appears with a
Smooth homology spheres and their fundamental groups
Let Mn be a smooth homology n-spherei, i.e. a smooth n-dimensional manifold such that H*(Mn) H*(S n). The fundamental group -a of M satisfies the following three conditions: (1) -a has a finite
Smooth manifolds with prescribed rational cohomology ring
The Hirzebruch signature formula provides an obstruction to the following realization question: given a rational Poincaré duality algebra $${\mathcal {A}}$$A, does there exist a manifold M such that
Topological methods in algebraic geometry
Introduction Chapter 1: Preparatory material 1. Multiplicative sequences 2. Sheaves 3. Fibre bundles 4. Characteristic classes Chapter 2: The cobordism ring 5. Pontrjagin numbers 6. The ring