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Results tagged with at.algebraic-topology
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user 20516
Homotopy theory, homological algebra, algebraic treatments of manifolds.
2
votes
Is there a homotopy/homology-theory for probability spaces?
The question needs be expressed in categorical terms.
The category of topology $TOP$ consists of objects and morphisms being topological spaces and continuous maps, respectively. Homology and homotopy …
- 2,274
3
votes
Accepted
Can we foliate the punctured space by tori?
I would like to offer another explanation of the impossibility of foliating $R^3-0$ by tori (or by higher genus closed surfaces), at least in the $C^\infty$ case.
Previously I commented that "folia …
- 2,274
2
votes
Relation between optimal transport cost and difference between topological invariants?
Applications of OT to Algebraic Topology was the subject of my thesis available here https://github.com/jhmartel/Thesis2019
There remains many interesting questions to solve!
I found the topology of e …
- 2,274
2
votes
Fundamental groups of noncompact surfaces
A new approach to spines is available via mass transport theory and Kantorovich duality. This is developed in my PhD thesis.
The idea is elementary: consider the retract $x\mapsto x/|x|$ from the cl …
- 2,274