Aleksandar Milivojevic
Graduate student
I am a thirdyear graduate student, interested mostly in algebraic topology. I think about rational homotopy theory, characteristic classes, and four manifolds.
My advisor is Dennis Sullivan.
You can find my CV here.

Email: milivojevic[at]math.stonybrook.edu

Office: 3104, Math Department, Stony Brook University
Some short notes (informal)
All manifolds are (unless otherwise stated) smooth, closed, and connected. Spaces have the homotopy type of a finite or countable cell complex. Minimal models are in the
sense of rational homotopy theory.
Some computations with the Froelicher spectral sequence.
A discussion on almostcomplex and stablyalmostcomplex structures, and
the obstructions to such structures in low dimensions. You can find the
minimal models of some relevant homogeneous spaces SO(2n)/U(n)
here. And believe it or not,
not all homogeneous spaces are formal.
The rational homotopy type of the space of almost complex structures on the sixsphere.
A word on cohomologically split fibrations.
Simply connected manifolds of dimension six or less are formal.
A nilmanifold is a torus iff all of its triple
Massey products vanish.
Closed Lie groups are rationally products of odd spheres.
A symplectic nonKaehler complex threefold all of whose
odd Betti numbers are even, and an almostcomplex four manifold with no
complex structure.
The minimal model of the free loop space of a simply connected space, and an
application.
The minimal models of the complex Grassmannians G(2,4), G(2,5), G(2,6), G(3.6),
and those of CP2#CP2 and CP2#CP2.
Representing cohomology of lowdimensional manifolds by maps to other manifolds.
The secondtolast StiefelWhitney class of a 4k manifold vanishes.
Other
A 1975 paper by Deligne and Sullivan, Complex vector bundles with discrete structure group,
translated from French to English. Here you can find the original.
A brief review of the more topologicallyoriented chapters in Freed and
Uhlenbeck's "Instantons and Four Manifolds".


