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How to show that $M:=\{(a,b,c)\in\Bbb R^3 \,\,∣\,\,a^3+b^3+c^3−3abc=1\}$ is not a compact space?

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#algebraic-geometry #complex-numbers #differential-topology #geometric-topology
50
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Equivalent surgeries

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#geometric-topology #knot-theory
526
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Prove that on any manifold $M$ there exists a proper smooth map $f: M \to \mathbb R.$

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#smooth-manifolds #geometric-topology
94
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line bundles and spheres

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#differential-geometry #differential-topology #geometric-topology
104
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Proving that some $\pi_i(M^3)$ vanishes using net multiplicity

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#homology-cohomology #geometric-topology
43
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A criterion for linear independence of curves in a surface

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#linear-algebra #surfaces #geometric-topology
264
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Hairy ball theorem for beginners

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#multivariable-calculus #reference-request #differential-topology #book-recommendation #geometric-topology
58
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Unknot is fibred

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#geometric-topology #knot-theory
329
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Open simply connected covering implies simply connectedness of the space

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#algebraic-topology #geometric-topology
248
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Proof that such a set is a smooth submanifold.

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#differential-geometry #smooth-manifolds #geometric-topology
322
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Prime decomposition of manifolds

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#algebraic-topology #geometric-topology
374
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Fundamental group of a Cayley graph

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#group-theory #geometric-topology #geometric-group-theory
1.2k
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Manifolds Resulting from Gluing Tori

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#general-topology #algebraic-topology #geometric-topology
99
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Open Book Decompositions of 3-manifold and Associated Heegard Splittings

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#general-topology #algebraic-topology #geometric-topology
146
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handle moves: proof

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#reference-request #differential-topology #geometric-topology #low-dimensional-topology #morse-theory

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