Intereting Posts

How to find complex numbers $z,\lambda,\mu$ such that $(z^\lambda)^\mu\neq z^{\lambda\mu}$
An axiomatic treatment of hyperbolic trigonometry?
Rational Point in circle
Group where every element is order 2
Proof related to breadth first search
Number made from ending digits of primes
Is $\mathbb{R}/(P)$ isomorphic to $\mathbb C$ for every irreducible polynomial $P$ of degree $2?$
Integral $\int_0^\infty \frac{\sin x}{\cosh ax+\cos x}\frac{x}{x^2-\pi^2}dx=\tan^{-1}\left(\frac{1}{a}\right)-\frac{1}{a}$
Cheap proof that the Sorgenfrey line is normal?
Singular values of transpose same?
Create a formula that creates a curve between two points
Intuitively, how should I think of Measurable Functions?
Prove that if $R$ is von Neumann regular and $P$ a prime ideal, then $P$ is maximal
$\binom{p}{i}$ divisible by $p$, with $p$ prime
A Math function that draws water droplet shape?

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.

- CW complex such that action induces action of group ring on cellular chain complex.
- Splitting of the tangent bundle of a vector bundle
- Is the quotient map a homotopy equivalence?
- Homology groups of torus
- Extending to a disc means fundamental group is trivial
- Is $\operatorname{Aut}(\mathbb{I})$ isomorphic to $\operatorname{Aut}(\mathbb{I}^2)$?

Can you help me?

- How to show $S^n$ is not contractible without using Homology..
- Understanding the trivialisation of a normal bundle
- Applications for Homology
- Does a morphism between covering spaces define a covering?
- Are these two spaces homotopy equivalent?
- A(nother ignorant) question on phantom maps
- Globally generated vector bundle
- Does homotopy equivalence of pairs $f:(X,A)\to(Y,B)$ induce the homotopy equivalence of pairs $f:(X,\bar A)\to(Y,\bar B)$?
- Simplicial Complexes, Triangulation general question.
- Conjugacy Class of Isomorphisms Between Two Isomorphic Groups Definition

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 $H:E \times [0,1] \to E$.

- Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
- Constructive proof of boundedness of continuous functions
- Determine all real polynomials with $P(0)=0$ and $P(x^2+1)=(P(x))^2+1$
- Show that $\rm lcm(a,b)=ab \iff gcd(a,b)=1$
- What is the correct way to think about this yet another balls/boxes problem?
- Prove that the set of all algebraic numbers is countable
- If $x$ is a positive integer such that $x(x+1)(x+2)(x+3)+1=379^2$, find $x$
- A strange puzzle having two possible solutions
- sets with no asymptotical density over $\mathbb N$
- A “Trivial” Smooth Structure
- What are the $n$th roots of the identity function?
- Prime Divisors of $x^2 + 1$
- What does limit notation with an underline or an overline mean?
- Is it possible that the zeroes of a polynomial form an infinite field?
- A function is continuous if its graph is closed