Seminarium z Topologii Algebraicznej
Wtorki, 12:15-13:45, sala 4070
3.XII.2013
Dikran Karagueuzian (Binghamton University)
Conjectures uniting Free Actions on Manifolds with Commutative Algebra
The Buschsbaum-Eisenbud-Horrocks conjecture asserts that the Koszul resolution is the "smallest possible resolution" in the sense that any resolution of a dimension-zero graded module over a polynomial ring has Betti numbers which are at least as large.
A well-known conjecture in transformation groups states that a product of spheres is the "most symmetric possible compact manifold", in the sense that if an elementary abelian p-group of rank r acts freely on a compact manifold then the mod-p homology of that manifold has total dimension at least 2^r. (That is, at least as large as that of the product of r spheres.)
We will discuss efforts to unify these conjectures in the context of differential graded modules. There is less progress on the unification than on the individual conjectures and the talk will be mostly expository.