Roman Mikhailov
On the splitting of polynomial functors.
Пнд, 02/06/2012 - 15:01 — SomNambulAuthors: Roman Mikhailov
Subjects: Algebraic Topology
AbstractWe develop methods for proving that certain extensions of polynomial functors
do not split naturally. As an application we give a functorial description of
the third and the fourth stable homotopy groups of the classifying spaces of
free abelian groups.Symmetric ideals in group rings and simplicial homotopy.
Втр, 02/02/2010 - 16:01 — SomNambulAuthors: Roman Mikhailov, Jie Wu, Inder Bir S. Passi
Subjects: Group Theory
AbstractIn this paper homotopical methods for the description of subgroups determined
by ideals in group rings are introduced. It is shown that in certain cases the
subgroups determined by symmetric product of ideals in group rings can be
described with the help of homotopy groups of spheres.On the homology of the dual de Rham complex.
Втр, 01/19/2010 - 16:01 — SomNambulAuthors: Roman Mikhailov
Subjects: Algebraic Topology
AbstractWe study the homology of the dual de Rham complex as functors on the category
of abelian groups. We give a description of homology of the dual de Rham
complex up to degree 7 for free abelian groups and present a corrected version
of the proof of Jean's computations of the zeroth homology group.Derived functors of non-additive functors and homotopy theory.
Пт, 10/16/2009 - 17:25 — SomNambulAuthors: Roman Mikhailov, Lawrence Breen
Subjects: Algebraic Topology
AbstractWe develop a functorial approach to the study of the homotopy groups of
spheres and Moore spaces $M(A,n)$, based on the Curtis spectral sequence and
the decomposition of Lie functors as iterates of simpler functors such as the
symmetric or exterior algebra functors. The discussion takes place over the
integers, and includes a functorial description of the derived functors of
certain Lie algebra functors, as well as of all the main cubical functors (such
as the degree 3 component $SP^3$ of the symmetric algebra functor).- Читать далее
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On homotopy groups of the suspended classifying spaces.
Ср, 08/26/2009 - 14:58 — SomNambulAuthors: Roman Mikhailov, Jie Wu
Subjects: Algebraic Topology
AbstractIn this paper, we determine the homotopy groups $\pi_4(\Sigma K(G,1))$,
$\pi_5(\Sigma K(G,1))$ and $\pi_5(\Sigma^2K(G,1))$ for different groups $G$ by
using different facts and methods from group theory and homotopy theory:
derived functors, the Carlsson simplicial construction, the Baues-Goerss
spectral sequence, homotopy decompositions and the methods of algebraic
K-theory.
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