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A space that deformation retracts into the cylinder and Möbius band doesn't embed in $\Bbb R^3$.

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#general-topology #algebraic-topology #orientation #non-orientable-surfaces
3.5k
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Why is Klein bottle non-orientable?

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#general-topology #differential-geometry #klein-bottle #mobius-band #non-orientable-surfaces
1.6k
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Orientable Surface Covers Non-Orientable Surface

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#algebraic-topology #surfaces #covering-spaces #non-orientable-surfaces
1.7k
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If a smooth, compact, connected manifold $M$ is not orientable then its top De Rham cohmology is zero

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#differential-geometry #manifolds #differential-forms #de-rham-cohomology #non-orientable-surfaces
1k
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Fixed points in mapping from Möbius strip to disk [Explanation or reference needed]

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#general-topology #differential-topology #surfaces #orientation #non-orientable-surfaces
674
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Non-orientable cover of a non-orientable surface

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#algebraic-topology #surfaces #covering-spaces #low-dimensional-topology #non-orientable-surfaces
825
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Cell decomposition of non-orientable surfaces

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#general-topology #non-orientable-surfaces
81
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Surface identification and fundamental group.

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#general-topology #algebraic-topology #fundamental-groups #non-orientable-surfaces
248
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Surface identification of hexagon with some edges identified.

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#general-topology #algebraic-topology #non-orientable-surfaces
89
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maps on quotients.

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#geometry #algebraic-topology #quotient-spaces #klein-bottle #non-orientable-surfaces
143
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Construct a generic unorientable surfaces of genus $g$

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#differential-geometry #differential-topology #riemann-surfaces #geometric-topology #non-orientable-surfaces
275
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2-dimensional manifold is orientable if and only if it does not contain the Möbius band

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#differential-geometry #smooth-manifolds #mobius-band #non-orientable-surfaces
422
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How exactly a crosscap relates to a Mobius strip, $^2$, and Klein bottle

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#algebraic-topology #manifolds #differential-topology #non-orientable-surfaces #generalized-topology
871
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Why is the genus (in terms of Euler characteristic) the maximum number of disj. closed curves that can be embedded in a surface without separating it?

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#general-topology #surfaces #geometric-topology #non-orientable-surfaces
196
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Is it always possible to extend a homeomorphism from a closed ball in the plane onto a closed disk in a surface to their neighbourhoods?

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#general-topology #surfaces #geometric-topology #non-orientable-surfaces

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