turkmath.org

In transformation group theory, there is a well known conjecture which states that if G=(Z/pZ)^r acts freely on a product of k spheres, then r is less than or equal to k. Carlsson states another conjecture which is even stronger than this conjecture; if C is a finite complex of free F_p[G] modules with nonzero homology, then dim_k H_*(C) is greater than or equal to 2^r. In this talk, we will discuss a conjecture which is equivalent to Carlsson’s conjecture for p=2 by considering differential graded modules over a polynomial ring in r variables over a field of characteristic 2. This is the first talk of a series of seminars on this topic which we plan to give during this semester.