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Atiyah-(Patodi)-Singer index theorem and an instanton on $S^5$

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#differential-geometry #differential-topology #mathematical-physics #geometric-topology #fermi-dirac-integral
318
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Can every smooth scalar function $f$ on $M$ be written as $f=\operatorname{div}(X)$?

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#differential-geometry #differential-topology #riemannian-geometry #de-rham-cohomology
49
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Question in the appendixes A of O'Neill book

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#differential-geometry #differential-topology #riemannian-geometry #semi-riemannian-geometry
41
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Basis for $\mathfrak{sl}(2,R)$ in terms of coordinate basis (or vice versa)

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#differential-geometry #differential-topology #lie-groups #lie-algebras
89
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Finding the inverse of a (challenging) function

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#algebra-precalculus #differential-topology #elementary-functions
405
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Under what conditions can one glue together local diffeomorphisms?

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#differential-geometry #differential-topology #smooth-manifolds
227
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Morse and Conley theory: Proof of finite rank for certain cohomology groups

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#algebraic-topology #differential-topology #dynamical-systems #homology-cohomology #morse-theory
205
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Existence of a special homotopy between two smooth loops

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#differential-topology #smooth-manifolds #homotopy-theory
431
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Definition of Integral over Manifolds

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#integration #manifolds #differential-topology
870
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Why does the Gauss-Bonnet theorem seem to work for some square boundary identifications but not others?

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#general-topology #differential-geometry #differential-topology #surfaces #projective-space
2.1k
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Critical Points of a smooth map on a compact manifold

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#manifolds #differential-topology #compact-manifolds
119
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Computing the differential of this map

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#multivariable-calculus #differential-geometry #differential-topology #lie-groups #lie-algebras
116
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Induced stable framing on circles

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#algebraic-topology #differential-topology #homotopy-theory #geometric-topology
255
Views

Motivations of studying $C^r$ manifolds when $r<\infty$

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#differential-geometry #differential-topology
754
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Can we extend any flat metric on the torus to a "standard" global flat metric?

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#differential-geometry #differential-topology #riemannian-geometry #symmetry

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