Nansen Petrosyan
Characteristic classes for cohomology of split Hopf algebra extensions.
Втр, 02/02/2010 - 16:01 — SomNambulAuthors: Nansen Petrosyan, Dieter Degrijse
Subjects: Algebraic Topology
AbstractWe introduce characteristic classes for the spectral sequence associated to a
split short exact sequence of Hopf algebras. We show that these characteristic
classes can be seen as obstructions for the vanishing of differentials in the
spectral sequence and prove a decomposition theorem. We also interpret our
results in the settings of group and Lie algebra extensions and prove some
interesting corollaries concerning the collapse of the
(Lyndon-)Hochschild-Serre spectral sequence and the order of characteristic
classes.New Action-Induced Nested Classes of Groups and Jump (Co)homology.
Ср, 11/04/2009 - 16:01 — SomNambulAuthors: Nansen Petrosyan
Subjects: Algebraic Topology
AbstractUsing fixed-point-free group actions, we set up a scheme to define nested
classes of groups indexed over ordinals. Restricting to cellular actions on
CW-complexes, we find new classes as well as new characterizations for some
well-known classes, such as virtually polycyclic groups. We generalize
properties of the virtual cohomological dimension of a group to groups with
jump (co)homology and prove that a core subclass of a new class of groups has
jump (co)homology.
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