NonExistence of Manifold structure on topological constructions

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.