Unit · year 4
MU-401 · Algebraic Topology
Threads space · structure4 theorems
Algebraic invariants that distinguish spaces up to deformation.
Theorems in this unit
T-118
The fundamental group
Loops up to homotopy form a group invariant of the space.
T-119
The Seifert–van Kampen theorem
The fundamental group of a union from those of its pieces.
T-120
The Brouwer fixed-point theorem
Every continuous self-map of a disc has a fixed point.
T-121
Invariance of the Euler characteristic
V−E+F is a topological invariant.