Let X be a finite aspherical CW-complex whose fundamental group π1(X) possesses a subnormal series π1(X) ⊲ Gm ⊲ . . . ⊲ G0 with a non-trivial elementary amenable group G0. We investigate the L2-invariants of the universal covering of such a CW-complex X. We show that the NovikovShubin invariants αn(X̃) are positive. We further prove that the L2-torsion ρ(2)(X̃) vanishes if π1(X) has semi-integral...

We continue the investigation of CW homotopy type of spaces of continuous functions between two CW complexes begun by J. Milnor in 1959 and P. Kahn in 1984. Viewing function spaces as particular cases of inverse limits we also study certain inverse systems of fibrations between CW homotopy type spaces. If the limit space Z∞ of an inverse sequence {Zi} of fibrations between CW type spaces has CW...

We construct a finite 1-connected CW complex X such that H * (ΩX; Z) has p-torsion for the infinitely many primes satisfying p ≡ 5, 7, 17, 19 mod 24, but no p-torsion for the infinitely many primes satisfying p ≡ 13 or 23 mod 24. A homology torsion prime for a topological space Y is a prime p such that H * (Y ; Z) has p torsion. In [3] and [4] respectively, D. Anick and L. Avramov constructed s...

In recent work, Clark and Tchernev introduced the notion of monomial resolution supported on a poset. In this talk, I will review this notion, and the related notion of monomial resolution supported on a CW complex. I will discuss a result of mine that shows that resolutions supported on a CW complex are also supported on the face poset of a CW complex. This relates to the work of Clark and Tch...

It is proved that the critical cells of a discrete Morse function in the sense of Forman on a finite regular CW complex can always be detected by a polyhedral Morse function in the sense of Banchoff on an appropriate embedding in Euclidean space of the barycentric subdivision of the complex. The proof is stated in terms of discrete Morse functions on a class of posets that is slightly broader t...

It is proved that every discrete Morse function in the sense of Forman on a finite regular CW complex can be represented by a polyhedral Morse function in the sense of Banchoff on an appropriate embedding in Euclidean space of the barycentric subdivision of the CW complex; such a representation preserves critical points. The proof is stated in terms of discrete Morse functions on posets.

‎in this paper‎, ‎we prove the nonexistence of two weighing matrices of‎ ‎weight 81‎, ‎namely $cw(88,81)$ and $cw(99,81)$‎. ‎we will apply two‎ ‎very different methods to do so; for the case of $cw(88,81)$‎, ‎we‎  ‎will use almost purely counting methods‎, ‎while for $cw(99,81)$‎, ‎we‎ ‎will use algebraic methods‎.

Chain complexes with a group of operators are a well known tool in algebraic topology, where they arise naturally as the chain complex C∗X̃ of cellular chains of the universal cover X̃ of a reduced CW -complex X. The group of operators here is the fundamental group of X. J.H.C. Whitehead in his classical but little read paper [31] showed that the chain complex C∗(X̃) is useful for the homotopy cla...

Let F∗(X,Y) be the space of base-point-preserving maps from a connected finite CW complex X to a connected space Y . Consider a CW complex of the form X∪αe and a space Y whose connectivity exceeds the dimension of the adjunction space. Using a Quillen–Sullivan mixed type model for a based mapping space, we prove that, if the bracket length of the attaching map α : Sk → X is greater than the Whi...