Intereting Posts

Showing the polynomials are a basis of $P_2$
How to prove $n^5 – n$ is divisible by 30 without reduction
Understanding the proof of “$\sqrt{2}$ is irrational” by contradiction.
Understanding quotient groups
Intuitive understanding of the Reidemeister-Schreier Theorem
The cardinality of $\mathbb{R}/\mathbb Q$
When is $\Bbb{Z}$ a PID?
Evaluate $\tan ^{2}20^{\circ}+\tan ^{2}40^{\circ}+\tan ^{2}80^{\circ}$
Proving that an integral is differentiable
Complicated exercise on ODE
Expected number of coin tosses needed until all coins show heads
Structure theorem for finitely generated abelian groups
Is there a branch of mathematics that studies the factors of rational numbers?
Visualizing topology of a Vector Bundle
Is a factorial-primorial mesh ever divisible by the primorial?

I’m trying to prove the following:

Total space of vector bundle deformation retracts onto 0-section of base space.

Books seem to take this fact for granted. I checked Bott Tu and Hatcher. Online people are saying this is easy. I can’t figure it out. It’s easy to see that locally this is true. The total space has local trivializations and $\mathbb{R}^n$ deformation retracts onto $0$. I can’t think of a way to patch up these deformation retractions to get a global one on the total space. I tried using partitions of unity to no avail.

- Easier proof about suspension of a manifold
- Embedding a manifold in the disk
- Top Cohomology group of a “punctured” manifold is zero?
- Fundamental group of projective plane is $C_{2}$???
- $n$-dimensional holes
- Homology of connected sum of real projective spaces

Can you help me?

- When does a continuous map $f:X\rightarrow \mathbb{H}P^n$ lift to $S^{4n+3}$?
- Formula relating Euler characteristics $\chi(A)$, $\chi(X)$, $\chi(Y)$, $\chi(Y \cup_f X)$ when $X$ and $Y$ are finite.
- Topological Conditions Equivalent to “Very Disconnected”
- The blow up of of the plane and the Moebius band
- Seifert matrices and Arf invariant — Cinquefoil knot
- Line bundles of the circle
- Proof category of $k$-spaces is “almost” locally Cartesian closed
- (Certain) colimit and product in category of topological spaces
- $I^2$ does not retract into comb space
- CW complex structure of the projective space $\mathbb{RP}^n$

Scalar multiplication $v \mapsto (1 – t)v$ commutes with arbitrary linear transformations, in particular with transition functions.

Consequently, if $E$ denotes the total space of your vector bundle, $x$ denotes a local coordinate on the base, and $v$ denotes a local coordinate in the fibres, the formula $H(x, v, t) = \bigl(x, (1 – t)v\bigr)$ is independent of trivialization, and so defines a deformation retraction $H:E \times [0,1] \to E$.

- Write $1/1 + 1/2 + …1/ (p-1)=a/b$ with $(a,b)=1$. Show that $p^2 \mid a$ if $p\geq 5$.
- How many number of functions are there?
- Computing the ring of integers of a number field $K/\mathbb{Q}$: Is $\mathcal{O}_K$ always equal to $\mathbb{Z}$ for some $\alpha$?
- Evaluating $\displaystyle \int_{0}^{\frac{\pi}{2}}\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}dx$
- Product of all monic irreducibles with degree dividing $n$ in $\mathbb{F}_{q^n}$?
- Definition of a tensor for a manifold
- How could I improve this approximation?
- What is the sum of this series? $\sum_{n=1}^\infty\frac{\zeta(1-n)(-1)^{n+1}}{2^{n-1}}$
- Complex Numbers on a Circle – Challenging Problem
- Automorphisms of the Petersen graph
- The subset of non-measurable set
- Isomorphism of an endomorphism ring, how can $R\cong R^2$?
- Dijkstra's algorithm proof
- 2-norm vs operator norm
- Prove that the kernel of a homomorphism is a principal ideal. (Artin, Exercise 9.13)