Intereting Posts

Summation of a function 2
Prove $R \times R$ is NOT an integral domain
Any even elliptic function can be written in terms of the Weierstrass $\wp$ function
Linear transformation preserving orthogonality
nilpotent elements of $M_2(\mathbb{R})$, $M_2(\mathbb{Z}/4\mathbb{Z})$
Examples of nowhere continuous functions
Embedding of Kähler manifolds into $\Bbb C^n$
Find maximum divisors of a number in range
Proving Cauchy's Generalized Mean Value Theorem
Do limits of sequences of sets come from a topology?
$\mathbb R^2$ is not homeomorphic to $\mathbb R^3$.
Find the maximum and minimum radii vectors of section of the surface $(x^2+y^2+z^2)^2=a^2x^2+b^2y^2+c^2z^2$ by the plane $lx+my+nz=0$
What is the Galois group of the splitting field of $X^8-3$ over $\mathbb{Q}$?
Contradiction achieved with the Pettis Measurability Theorem?
Find the derivative of the inverse of this real function $f(x) = 2x + \cos(x)$

i have some problems with the exercise 2.2.6 in hatcher book “algebraic topology“. Hope that someone could help me out. One has to show that every map $S^{n} \rightarrow S^{n}$ can be homotoped to a map with a fixed point. Hope this is not too trivial. Thanks in advance.

beno

- Surface of genus $g$ does not retract to circle (Hatcher exercise)
- Does the Euler characteristic of a manifold depend upon the field of coefficients?
- Cup Product Structure on the Projective Space
- Intuitive Aproach to Dolbeault Cohomology
- Showing that a zigzag space is contractible
- Holomorphic functions on a complex compact manifold are only constants

- Does the rank of homology and cohomology groups always coincide?
- Can one prove that the fundamental group of the circle is $\mathbb Z$ without using covering spaces?
- map of arbitrary degree from compact oriented manifold into sphere
- What are other examples of characteristic numbers?
- Existence of a universal cover of a manifold.
- Two homologous but not homotopic loops on a closed surface of genus greater than one
- CW complexes and manifolds
- Obstructions to lifting a map for the Hopf fibration
- Hatcher chapter 0 exercise.
- cohomology of tensor product of a vector space with a double complex

One thing that is proved in that section is that any map without fixed points can be homotoped to the antipodal map. So it remains only to show that the antipodal map is homotopic to a map with a fixed point. A particular example of a homotopy is composition with a family of rotations. So the antipodal map is homotopic to its composition with a half rotation through some axis. Now does this map have any fixed points?

- lebesgue integral uniform convergence
- Visual Ways to Remember Cross products of Unit vectors? Cross-product in $\mathbb F^3$?
- Divisibility by 7
- Interpretation of eigenvectors of cross product
- $A = \bigcap_{\mathfrak{p} \in \text{Spec(A)}} A_{\mathfrak{p}} = \bigcap_{\mathfrak{m} \in \text{MaxSpec(A)}} A_{\mathfrak{m}}$
- Trigonometric Equation $\sin x=\tan\frac{\pi}{15}\tan\frac{4\pi}{15}\tan\frac{3\pi}{10}\tan\frac{6\pi}{15}$
- Does $\sum_{n\ge1} \sin (\pi \sqrt{n^2+1}) $ converge/diverge?
- Represent a Uniform random variable as a sum of independent Bernoulli(1/2) random variables
- Clarifying on how if p,q is logically equivalent to p only if q
- $\forall A\subset \mathbb{N}$ the sum of the reciprocals of $A$ diverges iff $A$ is $(\tau, \mathbb{N})$-dense
- What is the “taxonomy” or “hierarchy” (partial ordering) of algebraic objects used to attempt to capture geometric intuition?
- Does the improper integral $\int_0^\infty e^{-x^2}dx$ converge?
- $U^*\otimes V$ versus $L(U,V)$ for infinite dimensional spaces
- The relationship between tan(x) and square roots
- Are there different ways to embed surface with nonvanishing curvature in a higher-dimensional Euclidean space?