A simplicial monotone-light factorization theorem
An effective criterion for the existence of a mass partition
Applications of knot theory in fluid mechanics
In this paper we present an overview of some recent results on applications of knot theory in fluid mechanics, as part of a new discipline called `topological fluid mechanics' (TFM). The choice of the topics covered here is deliberately restricted to those areas that involve mainly a combination of ideal fluid mechanics techniques and knot theory concepts, complemented with a brief description of some other concepts that have important applications in fluid systems. We begin with the concept of...
Counting connected components of the complement of the image of a codimension 1 map
Coverings and ring-groupoids.
Die Euler-Poincaré-Charakteristik und ihre topologische Weiterentwicklung.
Eine Verallgemeinerung zum Jordan-Brouwerschen Satz.
Groupoids, the Phragmen-Brouwer property, and the Jordan curve theorem.
Homotopy separators and mappings into cubes
M. M. Postnikov: his life, work and legacy
Measurable cardinals and fundamental groups of compact spaces
We prove that all groups can be realized as fundamental groups of compact spaces if and only if no measurable cardinals exist. If the cardinality of a group G is nonmeasurable then the compact space K such that G = π₁K may be chosen so that it is path connected.
On locally simply connected toposes and their fundamental groups
On the homological category of 3-manifolds.
Let M be a closed, connected, orientable 3-manifold. Denote by n(S1 x S2) the connected sum of n copies of S1 x S2. We prove that if the homological category of M is three then for some n ≥ 1, H*(M) is isomorphic (as a ring) to H*(n(S1 x S2)).
Some new results on composition of quadratic forms.
Steenrod's Equivariant Moore Space Problem for Cohomologically Trivial Modules.
The homology of spaces of simple topological measures
The simple topological measures X* on a q-space X are shown to be a superextension of X. Properties inherited from superextensions to topological measures are presented. The homology groups of various subsets of X* are calculated. For a q-space X, X* is shown to be a q-space. The homology of X* when X is the annulus is calculated. The homology of X* when X is a more general genus one space is investigated. In particular, X* for the torus is shown to have a retract homeomorphic to an infinite product...
Topological complexity of motion planning and Massey products
We employ Massey products to find sharper lower bounds for the Schwarz genus of a fibration than those previously known. In particular we give examples of non-formal spaces X for which the topological complexity TC(X) (defined to be the genus of the free path fibration on X) is greater than the zero-divisors cup-length plus one.
Two variants of Sperner's lemma with application to invariance of dimension theorems
Ueber einen Satz aus der Analysis situs
-cohomology manifold with no -resolution