3 citations · 4 across the 7 of their papers we have counts for
8 papers
Intersections of complex structures
Gustavo Granja, Aleksandar Milivojevic
We study the sets of planes in an even dimensional real vector space which are simultaneously stabilised by a pair of complex structures on . We completely describe these se…
Obstructions to almost complex structures following Massey
Michael Albanese, Aleksandar Milivojevic
We provide proofs of two theorems stated by Massey in 1961, concerning the obstructions to finding complex structures on real vector bundles. In addition, we determine the second o…
Verifying the Hilali conjecture up to formal dimension twenty
Spencer Cattalani, Aleksandar Milivojević
We prove that in formal dimension the Hilali conjecture holds, i.e. that the total dimension of the rational homology bounds from above the total dimension of the rationa…
On the topology of the space of almost complex structures on the six sphere
Bora Ferlengez, Gustavo Granja, Aleksandar Milivojevic
The space of orientation-compatible almost complex structures on the six-dimensional sphere naturally contains a copy of seven-dimensional real projective space. We show that the i…
On the realization of symplectic algebras and rational homotopy types by closed symplectic manifolds
Aleksandar Milivojevic
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 a…
Spin^h and further generalisations of spin
Michael Albanese, Aleksandar Milivojevic
The question of which manifolds are spin or spin^c has a simple and complete answer. In this paper we address the same question for spin^h manifolds, which are less studied but hav…
Connected sums of almost complex manifolds, products of rational homology spheres, and the twisted spin^c Dirac operator
Michael Albanese, Aleksandar Milivojevic
We record an answer to the question "In which dimensions is the connected sum of two closed almost complex manifolds necessarily an almost complex manifold?". In the process of doi…
On the minimal sum of Betti numbers of an almost complex manifold
Michael Albanese, Aleksandar Milivojevic
We show that the only rational homology spheres which can admit almost complex structures occur in dimensions two and six. Moreover, we provide infinitely many examples of six-dime…