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Is inner product a geodesically convex/concave function in $SO(3)$?

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#convex-analysis #manifolds #riemannian-geometry #smooth-manifolds
85
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If $f$ is a smooth function on a smooth manifold $M$ , then $df = 0$ if and only if $f$ is constant on each component of $M$

Published on
#analysis #differential-geometry #manifolds
31
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Dehn surgery on pseudomanifold to make bonafide manifold

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#manifolds #differential-topology #geometric-topology #klein-bottle #surgery-theory
128
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Vertical bundle and tangent bundle of the fiber

Published on
#differential-geometry #manifolds #differential-topology #vector-bundles #fiber-bundles
211
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Can the connected sum of three copies of $\mathbb{RP}^3$ be the total space of a fiber bundle?

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#algebraic-topology #manifolds #fiber-bundles #low-dimensional-topology
103
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Are these two definitions of smoothness on manifolds equivalent?

Published on
#manifolds #definition #smooth-manifolds #smooth-functions
91
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Prove/disprove that $X$ is a manifold

Published on
#algebraic-topology #manifolds #homology-cohomology #poincare-duality
440
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Homeomorphism vs Homotopy Equivalence

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#general-topology #geometry #algebraic-topology #manifolds
54
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A somewhat more general Regular Level Set theorem

Published on
#differential-geometry #manifolds
68
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Example of 2nd-countable T2 quotient of topological manifold that is not a topological manifold

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#general-topology #manifolds
171
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The boundary of any manifold that is itself a boundary of a higher-dimensional manifold must always be empty?

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#general-topology #manifolds #submanifold #manifolds-with-boundary
44
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What is the difference between a boundary *existing* (or rather, *not* existing) and a boundary *being empty*?

Published on
#general-topology #manifolds #submanifold #manifolds-with-boundary
42
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Manifold with "Distinct" Charts

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#general-topology #differential-geometry #manifolds
196
Views

What's the point of maximal atlases?

Published on
#category-theory #manifolds #differential-topology #smooth-manifolds
275
Views

Why are coordinate maps diffeomorphisms? (A seeming counterexample?)

Published on
#differential-geometry #manifolds #smooth-functions

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