NonExistence of Manifold structure on topological constructions
Mohammad Al Attar

TL;DR
This paper proves that certain topological constructions, such as wedges and cones of manifolds, do not possess manifold structures, using tools from homological algebra and algebraic topology.
Contribution
It establishes the non-existence of manifold structures on specific topological constructions like wedges and cones of manifolds.
Findings
Wedge of a manifold with itself is not a manifold.
Cone of a manifold is not a manifold.
Uses homological algebra and algebraic topology as main tools.
Abstract
We show the non existence of manifold structure on certain topological constructions. The main results of this paper are: (1) The wedge of manifold with itself is not a manifold. (2) The cone of a manifold is not a manifold. The main tools for the main result is homological algebra and algebraic topology.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Advanced Topology and Set Theory
