List questions from manifolds

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relative homology of manifold with boundary

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Manifold parallelizable equivalent condition

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List Question

Integral homology group of a 3-torus cut out a donut

Focal points in abstract sense

Finding an explicit smooth atlas for $GL_n(\mathbb{R})$

Show that the borel $\sigma$-algebra on $M$ is the unique $\sigma$-algebra whos restriction to each $U_\alpha$ is the pullback via $\pi_\alpha$

A submanifold of $\mathbb{R^2}$ (help with the rank)

What is an example of harmonic form on a compact manifold?

Smooth vector field on manifold and coordinate systems

Showing that $SO(2)$ is diffeomorphic(not just isomorphic as groups) to the circle

Differential of a one-form eating a vector?

Is it possible to have linked n-spheres in any other space other than $\Bbb R^{n+2}$?

Why are data points which are “close” should have a “similar” label?

relative homology of manifold with boundary

Nonvanishing vector field on an odd sphere

Existence of smooth vector field.

Manifold parallelizable equivalent condition

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