Generalized Poincare Conjecture

Tags: #projects/my-talks #open/conjectures

History

Poincaré, Analysis Situs papers in 1895. Coined “homeomorphism”, defined homology, gave rigorous definition of homotopy, established “method of invariants” and essentially kicked off algebraic topology.

Motivation

smooth structures

Background

See Algtop homotopy notes.

History

Motivation

[[smoothstructures.md|smooth structures]]

Background

See Algtop homotopy notes.

Other Topics

The homotopy hypothesis
cohomolology theories
[[cohomolology theories|generalized cohomology theory]]
Eilenberg-MacLane spaces
Homotopy Groups of Spheres

Links to this page

unresolved links output

The homotopy hypothesis in -Generalized Poincare Conjecture

cohomolology theories in -Arizona Winter School 2019, -Generalized Poincare Conjecture, -complex bordism, -complex oriented cohomology theory

homologysphere.md in -Generalized Poincare Conjecture

smoothstructures in -Generalized Poincare Conjecture
h-cobordism

Using h-cobordism to prove the Generalized Poincare Conjecture: File:Pasted image 20211103185616.png
Morse Theory

Can be used to prove the high dimensional case of the generalized Generalized Poincare Conjecture

#projects/my-talks #open/conjectures