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Do compact connected smooth manifolds admit the structure of a CW complex with a single 1-cell?

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#general-topology #algebraic-topology #differential-topology
145
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Transversality: what is wrong with this counter example to persistence for small perturbations?

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#differential-geometry #manifolds #differential-topology #dynamical-systems
153
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On Atiyah-Singer Index theorem and Atiyah-Bott fixed point theorem.

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#differential-geometry #partial-differential-equations #differential-topology #characteristic-classes #topological-k-theory
57
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Do smooth compact connected manifolds admit CW compositions with a single 0-cell?

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#general-topology #algebraic-topology #differential-topology
1.1k
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What is the tangent space o SO(n)

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#differential-geometry #manifolds #differential-topology #riemannian-geometry
159
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Parallel transport perspective of gauge transformation invariance for connections

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#differential-topology
160
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Low torsion in orientable manifolds?

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#algebraic-topology #manifolds #differential-topology #homology-cohomology #orientation
329
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A lemma in Milnor's book "Topology from the Differentiable Viewpoint"

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#differential-topology #implicit-function-theorem #compact-manifolds
160
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Condition for set of de Rham cohomology classes is linearly independent

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#differential-geometry #differential-topology #homology-cohomology #differential-forms #smooth-manifolds
347
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Understanding algebraic operations on vector bundles

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#differential-geometry #differential-topology #smooth-manifolds #vector-bundles
24
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open set in tangentspace induces open set in tangentbundle (for homogeneous spaces)

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#differential-geometry #differential-topology #homogeneous-spaces
660
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Frobenius theorem

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#differential-geometry #manifolds #differential-topology
181
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Vector field on n-manifold whose sum of indexes is equal to Euler charasteristic

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#algebraic-topology #differential-topology #homotopy-theory
804
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Solving the Euler-Lagrange equations for geodesics

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#ordinary-differential-equations #differential-geometry #differential-topology #geodesic
1.2k
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Orientability of $m\times n$ matrices with rank $r$

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#differential-geometry #differential-topology #smooth-manifolds #orientation

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