ﻻ يوجد ملخص باللغة العربية
If $G$ has $4$-periodic cohomology, then D2 complexes over $G$ are determined up to polarised homotopy by their Euler characteristic if and only if $G$ has at most two one-dimensional quaternionic representations. We use this to solve Walls D2 problem for several infinite families of non-abelian groups and, in these cases, also show that any finite Poincar{e} $3$-complex $X$ with $pi_1(X)=G$ admits a cell structure with a single $3$-cell. The proof involves cancellation theorems for $mathbb{Z} G$ modules where $G$ has periodic cohomology.
We determine the mod $2$ cohomology over the Steenrod algebra of the classifying spaces of the free loop groups $LG$ for compact groups $G=Spin(7)$, $Spin(8)$, $Spin(9)$, and $F_4$. Then, we show that they are isomorphic as algebras over the Steenrod
We present a detailed description of a fundamental group algorithm based on Formans combinatorial version of Morse theory. We use this algorithm in a classification problem of prime knots up to 14 crossings.
Let $pi$ be a group equipped with an action of a second group $G$ by automorphisms. We define the equivariant cohomological dimension ${sf cd}_G(pi)$, the equivariant geometric dimension ${sf gd}_G(pi)$, and the equivariant Lusternik-Schnirelmann cat
In this paper we study the cohomology of (strict) Lie 2-groups. We obtain an explicit Bott-Shulman type map in the case of a Lie 2-group corresponding to the crossed module $Ato 1$. The cohomology of the Lie 2-groups corresponding to the universal cr
The initial motivation of this work was to give a topological interpretation of two-periodic twisted de-Rham cohomology which is generalizable to arbitrary coefficients. To this end we develop a sheaf theory in the context of locally compact topologi