Stable homotopy classification of An4-polyhedra with 2- torsion free homology

We study the stable homotopy types of F_n~4(2)-polyhedra, i.e.,(n- 1)-connected, at most(n+ 4)-dimensional polyhedra with 2-torsion free homologies. We are able to classify the indecomposable F_n~4(2)-polyhedra. The proof relies on the matrix problem technique which was developed in the classification of representations of algebras and applied to homotopy theory by Baues and Drozd(1999, 2001, 2004).     

A link with Alexander module free which is not an homology boundary link

In this note is given an example of a 2-component ribbon link with trivial components, which has the same Alexander module as a trivial 2-component link and (hence) whose longitudes lie in the second commutator subgroup of the link group, yet which is not even an homology boundary link. This answers two questions raised by R.H. Fox and N.F. Smythe at the 1965 Wisconsin Topology Conference.     

Symplectic homology I open sets in ℂ n

Andreas Floer died on May 15, 1991. This is the one of several joint papers which were in preparation and are concerned with a symplectic homology theory     

An interpretation of E n -homology as functor homology

We prove that E _n -homology of non-unital commutative algebras can be described as functor homology when one considers functors from a certain category of planar trees with n levels. For different n these homology theories are connected by natural maps, ranging from Hochschild homology and its higher order versions to Gamma homology.     

The odd primary homology of SU(n), Sp(n) and Spin(n)-gauge groups

For an odd prime $p$, we calculate the mod-$p$ homology of $SU\left(n\right)$-gauge groups over a simply-connected, closed 4-manifold for all $n\ge 2$. Similar calculations are obtained for the structure groups $Sp\left(n\right)$ when $n\ge 1$ and $Spin\left(n\right)$ for $n\ge 3$ (except for some cases when $n$ is even and $p=3$).     

A Characterization of Astral (n 4 ) Configurations

A conjecture of Branko Grünbaum concerning what astral (n ₄ ) configurations exist is shown to be true. Received July 8, 2000, and in revised form February 14, 2001. Online publication August 28, 2001.     

Some examples of aspherical 4-manifolds that are homology 4-spheres

In this paper, Problem 4.17 on Kirby's problem list is solved by constructing infinitely many homotopy types of aspherical 4-manifolds that are homology 4-spheres.     

A problem with free boundary

One considers the Dirichlet problem for the equation u=(u), where is the Heaviside function. Under special assumptions one constructs the solution of this problem with convex and smooth level surfaces and, in particular, with a regular free surface, which coincides with the set of level zero. One proves the solvability in the small of the problem in the neighborhood of the constructed regular solution under perturbations of the boundary condition and a smooth boundary of the domain .Translated from Problemy Matematicheskogo Analiza, No. 10, pp. 72–83, 1986.     

Twisted second homology groups of the automorphism group of a free group

In this paper, we compute the second homology groups of the automorphism group of a free group with coefficients in the abelianization of the free group and its dual group except for the 2-torsion part, using combinatorial group theory.     

Twisted first homology groups of the automorphism group of a free group

The automorphism group and outer automorphism group of a free group F_n of rank n act on the abelianized group H of F_n and the dual group H^* of H. The twisted first homology groups of and with coefficients in H and H^* are calculated.     

Regular factors in K1,n free graphs

A graph is said to be K_1,n-free, if it contains no K_1,n as an induced subgraph. We prove that for n ? 3 and r ? n ?1, if G is a K_1,n-free graph with minimum degree at least (n²/4(n ?1))r + (3n ?6)/2 + (n ?1)/4r, then G has an r-factor (in the case where r is even, the condition r ? n ?1 can be dropped).     

On free semilattice-ordered semigroups satisfying x n =x

Let B(k,0,n) denote the group with k generators which is free in the group variety defined by the identity x ⁿ =1. Let B _slo (k,1,n) denote the semilattice-ordered semigroup with k generators which is free in the semilattice-ordered semigroup variety defined by the identity x ⁿ =x. We prove a generalization of the Green-Rees theorem: B _slo (k,1,n) is finite for all k≥1 if and only if B(k,0,n−1) is finite for all k≥1. We find a formula for card(B _slo (1,1,n)). We construct B _slo (k,1,n) for some concrete values of k and n.