Recently M. Kreck introduced a class of stratified spaces called p-stratifolds [M. Kreck, Stratifolds, Preprint]. He defined and investigated resolutions of p-stratifolds analogously to resolutions of algebraic varieties. In this note we study a very special case of resolutions, so called optimal resolutions, for p-str…
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10 results for “stratifolds”
Method counts connected 2D stratifolds with singular curves and components.
problem Counting -connected trivalent -stratifolds.
method Describes a method for counting.
result Counts -connected trivalent -stratifolds.
-stratifolds are a generalization of -manifolds that occur as objects in applications such as in TDA. These spaces can be described by an associated bicoloured labelled graph. In previous papers we obtained a classification of 1-connected trivalent -stratifolds. In this paper we classify trivalent -stratifo…
Trivalent -stratifolds are a generalization of -manifolds in that there are disjoint simple closed curves where three sheets meet. We obtain a classification of -connected -stratifolds in terms of their associated labeled graphs and develop operations that will construct from a single vertex all graphs that…
-stratifolds are a generalization of -manifolds in that there are disjoint simple closed branch curves. We obtain a list of all closed -manifolds that have a -stratifold as a spine.
-stratifolds are a generalization of -manifolds in that there are disjoint simple closed curves where several sheets meet. We show that the word problem for fundamental groups of -stratifolds is solvable.
2-dimensional stratifoldsmath.GT
2-stratifolds are a generalization of 2-manifolds in that there are disjoint simple closed curves where several sheets meet. They arise in the study of categorical invariants of 3-manifolds and may have applications to topological data analysis. We define 2-stratifolds and study properties of their associated labeled g…
Trivalent -stratifolds are a generalization of -manifolds in that there are disjoint simple closed curves where three sheets meet. We develop operations on their associated labeled graphs that will effectively construct from a single vertex all graphs that represent -connected -stratifolds. We describe an i…
Local systems in diffeologymath.AT
Introduces a framework for rational homotopy theory in diffeological spaces.
problem Challenges in rational homotopy theory for smooth spaces with arbitrary fundamental groups.
method Utilizes local systems over simplicial sets and a model structure for diffeological spaces.
result Establishes an equivalence between fibrewise rational diffeological spaces and algebraic local systems.
Hilbert stratifolds and a Quillen type geometric description of cohomology for Hilbert manifoldsmath.AT
In this paper we use tools from differential topology to give a geometric description of cohomology for Hilbert manifolds. Our model is Quillen's geometric description of cobordism groups for finite dimensional smooth manifolds \cite{Q}. Quillen stresses the fact that this construction allows the definition of Gysin ma…