A structured visual guide to the major mathematical areas and their relationships.
Search by code, branch, topic, subtopic, or a keyword from the descriptions.
This subtopic introduces the core ideas in pl-topology, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.
General topology of complexes. This topic develops PL-topology, where manifolds and maps are studied through piecewise-linear structures and triangulations.
Wikipedia: Piecewise-linear topology
Used to bridge purely topological and smooth viewpoints through combinatorial control.
Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion. This topic develops PL-topology, where manifolds and maps are studied through piecewise-linear structures and triangulations.
Wikipedia: Piecewise-linear topology
Used to bridge purely topological and smooth viewpoints through combinatorial control.
Wall's finiteness obstruction for CW-complexes. This topic develops PL-topology, where manifolds and maps are studied through piecewise-linear structures and triangulations.
Wikipedia: Piecewise-linear topology
Used to bridge purely topological and smooth viewpoints through combinatorial control.
Triangulating manifolds. This topic develops PL-topology, where manifolds and maps are studied through piecewise-linear structures and triangulations.
Wikipedia: Piecewise-linear topology
Used to bridge purely topological and smooth viewpoints through combinatorial control.
Cobordism in PL-topology. This topic develops PL-topology, where manifolds and maps are studied through piecewise-linear structures and triangulations.
Wikipedia: Piecewise-linear topology
Used to bridge purely topological and smooth viewpoints through combinatorial control.
Comparison of PL-topology with TOP or DIFF; combinatorial Pontryagin classes. This topic develops PL-topology, where manifolds and maps are studied through piecewise-linear structures and triangulations.
Wikipedia: Piecewise-linear topology
Used to bridge purely topological and smooth viewpoints through combinatorial control.
Engulfing in PL-topology. This topic develops PL-topology, where manifolds and maps are studied through piecewise-linear structures and triangulations.
Wikipedia: Piecewise-linear topology
Used to bridge purely topological and smooth viewpoints through combinatorial control.
Embeddings and immersions in PL-topology. This topic develops PL-topology, where manifolds and maps are studied through piecewise-linear structures and triangulations.
Wikipedia: Piecewise-linear topology
Used to bridge purely topological and smooth viewpoints through combinatorial control.
Isotopy in PL-topology. This topic develops PL-topology, where manifolds and maps are studied through piecewise-linear structures and triangulations.
Wikipedia: Piecewise-linear topology
Used to bridge purely topological and smooth viewpoints through combinatorial control.
Regular neighborhoods in PL-topology. This topic develops PL-topology, where manifolds and maps are studied through piecewise-linear structures and triangulations.
Wikipedia: Piecewise-linear topology
Used to bridge purely topological and smooth viewpoints through combinatorial control.
Knots and links in high dimensions. This topic develops PL-topology, where manifolds and maps are studied through piecewise-linear structures and triangulations.
Wikipedia: Piecewise-linear topology
Used to bridge purely topological and smooth viewpoints through combinatorial control.
Microbundles and block bundles. This topic develops PL-topology, where manifolds and maps are studied through piecewise-linear structures and triangulations.
Wikipedia: Piecewise-linear topology
Used to bridge purely topological and smooth viewpoints through combinatorial control.
Approximations in PL-topology. This topic develops PL-topology, where manifolds and maps are studied through piecewise-linear structures and triangulations.
Wikipedia: Piecewise-linear topology
Used to bridge purely topological and smooth viewpoints through combinatorial control.
Cobordism and concordance in PL-topology. This topic develops PL-topology, where manifolds and maps are studied through piecewise-linear structures and triangulations.
Wikipedia: Piecewise-linear topology
Used to bridge purely topological and smooth viewpoints through combinatorial control.
General position and transversality. This topic develops PL-topology, where manifolds and maps are studied through piecewise-linear structures and triangulations.
Wikipedia: Piecewise-linear topology
Used to bridge purely topological and smooth viewpoints through combinatorial control.
Equivariant PL-topology. This topic develops PL-topology, where manifolds and maps are studied through piecewise-linear structures and triangulations.
Wikipedia: Piecewise-linear topology
Used to bridge purely topological and smooth viewpoints through combinatorial control.
None of the above. This topic develops PL-topology, where manifolds and maps are studied through piecewise-linear structures and triangulations.
Wikipedia: Piecewise-linear topology
Used to bridge purely topological and smooth viewpoints through combinatorial control.