Spivak, Calculus on Manifolds, Problem 1-30
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Let $f$ be increasing on $[a,b]$ and $a < x_1 < \dotsb < x_n < b$. Show that $\sum_{k = 1}^n [f(x_k^+) - f(x_k^-)]\leq f(b^-) - f(a^+)$.
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The "Easiest" non-smoothable manifold
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Is it known what the necessary and sufficient conditions are for the existence of a "3+1 split" (by means of a foliation) of a (Lorentzian) manifold?
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Continuous map of differentiable manifolds is differentiable if differentiable functions pull back to differentiable functions
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Autohomeomorphism of the unit disk which is constant on the boundary, and which takes 0 to a prescribed point
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Torsion on $\pi_1(X)$, $X$ connected and open in $\mathbb{R}^n$
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Continuous maps between compact manifolds are homotopic to smooth ones
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example of a non differentiable manifold
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Spivak's Calculus - Exercise 4.a of 2nd chapter
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How to go about solving this question on differentials?
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Proving that the general linear group is a differentiable manifold
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Homology groups of $\mathbb{R}^3\setminus \ S^1$ and $\mathbb{R}^3\setminus E^1_+$
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Showing diffeomorphism between $S^1 \subset \mathbb{R}^2$ and $\mathbb{RP}^1$
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A PDE exercise from Gilbarg Trudinger. problem 2.2
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The only 1-manifolds are $\mathbb R$ and $S^1$
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Proving that given any two points in a connected manifold, there exists a diffeomorphism taking one to the other
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T$\mathbb{S}^{n} \times \mathbb{R}$ is diffeomorphic to $\mathbb{S}^{n}\times \mathbb{R}^{n+1}$