Time: 9h00, Wednesday, November 16, 2016
Location: Room 6, Building A14, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi
Abstract: Although the notion of an unstable module had appeared earlier in the work of Steenrod on the algebra that bears his name, the intensive study of unstable modules only begun after the works of Carlsson, Miller, Lannes, Schwartz and many others on the conjectures of Segal and Sullivan, two of the great highlights in algebraic topology in the late 1980’s and 1990’s, which led to the establishment of a whole new area within the subject. This talk aims at introducing the theory of unstable module with the emphasis on homological algebra aspects of the theory. In particular, we will recall various long exact sequences of unstable modules as well as the Bousfield construction of the algebraic EHP sequence. The EHP sequence is one of the most important tools in studying the E2−term of the unstable Adams spectral sequence (UASS), whose input takes the form of Ext-groups in the category of unstable modules. Nevertheless, lack of knowledge on the differentials of the sequence makes the computation complicated. To avoid this problem, we present, in the second part of the talk, a new technique called Pseudo-hyperresolution that allows for computing a large part of the E2−page of the UASS