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$f : M \longmapsto N \hspace{0.1cm} C^{\infty}$ if dim $M > $dim $N$ then $f$ can't be injective

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#manifolds #differential-topology #smooth-manifolds #manifolds-with-boundary
573
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What books would you recommend to understand gauge theories?

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#differential-geometry #differential-topology #physics #gauge-theory
161
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Relation between Morse number and Heegaard number

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#general-topology #differential-topology #morse-theory
63
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Smooth identification of the complement of a disk

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#general-topology #manifolds #differential-topology #smooth-manifolds #compact-manifolds
110
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Degree of the map $\mathbb{C} \times \mathbb{R} \longmapsto \mathbb{C} \times \mathbb{R}$ $: X(z,t) = (z^2,t)$

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#differential-geometry #manifolds #differential-topology #smooth-manifolds #vector-fields
128
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Integral of a $1$-form on $S^1$ with respect to a parametrization (Guillemin and Pollack, 4.4.6)

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#differential-geometry #differential-topology #differential-forms
225
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Covariant derivative do Carmo help clarification concept

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#differential-geometry #proof-explanation #differential-topology #riemannian-geometry
105
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Transitivity of Equivalence Relation of Tangent Vectors on Manifold

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#differential-topology #smooth-manifolds
526
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Why is Killing form $ad$-invariant?

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#differential-topology #lie-algebras
82
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$C^r$ submanifold of $C^r$ manifold

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#differential-geometry #differential-topology
213
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Complex conjugation map is not properly homotopic to the identity map of complex plane

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#algebraic-topology #differential-topology #homology-cohomology #geometric-topology #de-rham-cohomology
96
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Is $(\mathbb{C},+)$ isomorphic to a matrix Lie group?

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#differential-geometry #differential-topology #lie-groups #linear-groups
105
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Can one set and use some axioms for calculating intersection forms of manifolds?

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#algebraic-topology #differential-topology #homology-cohomology #4-manifolds
249
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Examples of non-compact 3-dim submanifolds with non-trivial normal bundle

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#differential-geometry #algebraic-topology #differential-topology
60
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$C^\infty$ Manifolds. Charts.

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#differential-geometry #manifolds #differential-topology

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