If $f:S^2\to S^2$ is homotopic to the identity does it have a fixed point?
8799
Mapping homotopic to the identity map has a fixed point
64084
Existence of a simple closed curve which is not null-homotopic
72044
prove $x \mapsto x^2$ is continuous
49924
Analytic map with two fixed points on a simply connected domain is the identity
129875
Fixed point theorem on spheres
30178
Homeomorphism $(\mathbb{CP}^1)^m/S_m \overset{\sim}{\to} \mathbb{CP}^m$?
32923
Homotopy equivalence of universal cover
60348
How do I prove $F(a)=F(a^2)?$
148187
Question regarding one-point compactification and homeomorphisms
124688
Question about a metric on $\mathbb{R}^2$
152451
REVISITED $^2$: Does a solution in $\mathbb{R}^n$ imply a solution in $\mathbb{Q}^n$?
156904
Homotopy Extension Property: necessary and sufficient condition
149390
Fixed point of a Function (monotonically increasing)
36402
Prove that $f(x) = \cos(x)$ has a unique fixed point.
139779
Homotopic maps have homotopy equivalent mapping cones
45276
Continuous map on $S^2$
126881
(weak) homotopy equivalence