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Differentiable structure on the real line

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If $f:M\rightarrow N$ is $C^{\infty}$, bijective, and everywhere non-singular, then $f$ is a diffeomorphism

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#differential-topology #manifolds
107
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A knot which intersects $S^2$ transversely once in 3-connected manifold

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#algebraic-topology #differential-topology #geometric-topology
243
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non-equivalent bundles

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#algebraic-topology #differential-topology
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Poincaré Lemma Contractible Hypothesis

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#differential-geometry #differential-topology #differential-forms
213
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Thom space 2 definitions

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#algebraic-topology #differential-topology
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Vector Field of Torus

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#differential-topology #vector-analysis
617
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A curve in a submanifold with a tangent vector not necessarily in the submanifold's tangent space

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#differential-geometry #differential-topology
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Uncountable disjoint union of $\mathbb{R}$

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#general-topology #differential-topology #manifolds
115
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Unit partition to produce smooth function from continuous ones

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#general-topology #differential-geometry #differential-topology
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Orthogonal complement of a vector bundle

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#differential-topology #vector-bundles
178
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Algebraic topology involved in the 1/4-pinched sphere theorem?

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#general-topology #algebraic-topology #differential-geometry #differential-topology
229
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A Couple of Normal Bundle Questions

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#differential-topology
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Continuous maps between compact manifolds are homotopic to smooth ones

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#differential-geometry #differential-topology #homotopy-theory
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"The space of all lines on a plane is an open Möbius Band."

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#algebraic-topology #manifolds #differential-topology

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