Newbetuts

$\{(x,y)\!\in\!\mathbb{B}^n; -\varepsilon\leq-\|x\|^2\!+\!\|y\|^2\leq\varepsilon\}\approx\mathbb{B}^k\!\times\!\mathbb{B}^{n-k}$

On a manifold, is the $L^p$ space of vector fields complete?

Is a compact, simply-connected 3-manifold necessarily $S^3$ with $B^3$'s removed?

Proving that $N$ is a manifold.

Can we approximate a vector field on the plane with non-vanishing vector fields in $L^2$?

Problem from "Differential topology" by Guillemin

Naturality of the pullback connection

How to tell which manifolds can be embedded in $\mathbb{R}^n$, for a given $n$?

There is no immersion of the Möbius band in the plane.

Restriction of smooth functions.

On the smooth structure of $\mathbb{R}P^n$ in Milnor's book on characteristic classes.

Intuition behind the Thom Isomorphism.

Projection formula, Bott and Tu

Euler Characteristic of fiber bundle using Differential Geometry

New posts in differential-topology

Finding a metric to make a certain curve a circle

Showing that Sobolev norms on manifolds are equivalent

Topological Open Mapping Theorem for mappings between different Euclidean dimensions?

Gradient nonzero extensions of a vector field on the circle

Bijective local isometry to global isometry

Compute $\chi(\mathbb{C}\mathrm{P}^2)$.

$\{(x,y)\!\in\!\mathbb{B}^n; -\varepsilon\leq-\|x\|^2\!+\!\|y\|^2\leq\varepsilon\}\approx\mathbb{B}^k\!\times\!\mathbb{B}^{n-k}$

On a manifold, is the $L^p$ space of vector fields complete?

Is a compact, simply-connected 3-manifold necessarily $S^3$ with $B^3$'s removed?

Proving that $N$ is a manifold.

Can we approximate a vector field on the plane with non-vanishing vector fields in $L^2$?

Problem from "Differential topology" by Guillemin

Naturality of the pullback connection

How to tell which manifolds can be embedded in $\mathbb{R}^n$, for a given $n$?

There is no immersion of the Möbius band in the plane.

Restriction of smooth functions.

On the smooth structure of $\mathbb{R}P^n$ in Milnor's book on characteristic classes.

Intuition behind the Thom Isomorphism.

Projection formula, Bott and Tu

Euler Characteristic of fiber bundle using Differential Geometry