Aleksandar MilivojevicGraduate student
I am a third-year 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.
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.
Simply connected manifolds of dimension six or less are formal.
Closed Lie groups are rationally products of odd spheres.
The minimal model of the free loop space of a simply connected space.
The minimal model of the complex Grassmannian G(2,4).
No hypersurface in projective five-space is zero in the oriented cobordism ring.
The second-to-last Stiefel-Whitney class of a 4k manifold vanishes.
Two six manifolds with the same cohomology groups, but different cohomology rings.
OtherA 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 topologically-oriented chapters in Freed and Uhlenbeck's "Instantons and Four Manifolds".