Parallelizability of Finite H-Spaces.
Partial homotopy type of finite two-complexes.
Partition complexes, duality and integral tree representations.
Partitions of unity in homotopy theory
Periodic equivariant Real k-theories have rational Tate theory.
Periodische Homöomorhismen Seifertscher Faserräume.
Phantom maps and purity in modular representation theory, I
Let k be a field and G a finite group. By analogy with the theory of phantom maps in topology, a map f : M → ℕ between kG-modules is said to be phantom if its restriction to every finitely generated submodule of M factors through a projective module. We investigate the relationships between the theory of phantom maps, the algebraic theory of purity, and Rickard's idempotent modules. In general, adding one to the pure global dimension of kG gives an upper bound for the number of phantoms we need...
P-localization of some classes of groups.
The aim for the present paper is to study the theory of P-localization of a group in a category C such that it contains the category of the nilpotent groups as a full sub-category. In the second section we present a number of results on P-localization of a group G, which is the semi-direct product of an abelian group A with a group X, in the category G of all groups. It turns out that the P-localized (GP) is completely described by the P-localized XP of X, A and the action w of X on A. In the third...
Poincaré duality and commutative differential graded algebras
We prove that every commutative differential graded algebra whose cohomology is a simply-connected Poincaré duality algebra is quasi-isomorphic to one whose underlying algebra is simply-connected and satisfies Poincaré duality in the same dimension. This has applications in rational homotopy, giving Poincaré duality at the cochain level, which is of interest in particular in the study of configuration spaces and in string topology.
Pointed and unpointed shape and pro-homotopy
Polyhedra with finite fundamental group dominate finitely many different homotopy types
In 1968 K. Borsuk asked: Does every polyhedron dominate only finitely many different shapes? In this question the notion of shape can be replaced by the notion of homotopy type. We showed earlier that the answer to the Borsuk question is no. However, in a previous paper we proved that every simply connected polyhedron dominates only finitely many different homotopy types (equivalently, shapes). Here we prove that the same is true for polyhedra with finite fundamental group.
Polyhedra with virtually polycyclic fundamental groups have finite depth
The notions of capacity and depth of compacta were introduced by K. Borsuk in the seventies together with some open questions. In a previous paper, in connection with one of them, we proved that there exist polyhedra with polycyclic fundamental groups and infinite capacity, i.e. dominating infinitely many different homotopy types (or equivalently, shapes). In this paper we show that every polyhedron with virtually polycyclic fundamental group has finite depth, i.e., there is a bound on the lengths...
Polynomial operations on stable cohomotopy.
Postnikov invariants of H-spaces
It is known that the order of all Postnikov k-invariants of an H-space of finite type is finite. This paper establishes the finiteness of the order of the k-invariants of X in dimensions m ≤ 2n if X is an (n-1)-connected H-space which is not necessarily of finite type (n ≥ 1). Similar results hold more generally for higher k-invariants if X is an iterated loop space. Moreover, we provide in all cases explicit universal upper bounds for the order of the k-invariants of X.
Power-cancellation of CW-complexes with few cells.
In this paper we use the fact that the rings of integer matrices have the power-substitution property in order to obtain a power-cancellation property for homotopy types of CW-complexes with one cell in dimensions 0 and 4n and a finite number of cells in dimension 2n.
Primitivity in torsion free cohomology Hopf algebras
Problem session.
Product and other fine structure in polynomial resolutions of mapping spaces.
Product splittings for p-compact groups
We show that a connected p-compact group with a trivial center is equivalent to a product of simple p-compact groups. More generally, we show that product splittings of any connected p-compact group correspond bijectively to algebraic splittings of the fundamental group of the maximal torus as a module over the Weyl group. These are analogues for p-compact groups of well-known theorems about compact Lie groups.
Profinite homotopy theory.