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15
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degree of gauss map for genus $g$ torus in $\mathbb{R}^{3}$

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#differential-geometry #manifolds #smooth-manifolds #compact-manifolds
84
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Intuitive explanation of degree

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#differential-geometry #manifolds #smooth-manifolds #smooth-functions #compact-manifolds
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
211
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Can dimension of manifolds be understood similarly to dimension of schemes?

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#algebraic-geometry #smooth-manifolds #krull-dimension #compact-manifolds
491
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Manifolds with Euler characteristic equal to $\pm 1$

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#algebraic-topology #homology-cohomology #compact-manifolds
121
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Prove that if $f:M\rightarrow\Bbb R$ is a scalar function over a 1-manifold M without boundary then $\int_M df=0$

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#calculus #multivariable-calculus #differential-geometry #stokes-theorem #compact-manifolds
266
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Graph embeddings on nonorientable surfaces

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#graph-theory #planar-graphs #compact-manifolds
83
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Irreducible triangulations of manifolds

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#manifolds #riemannian-geometry #simplicial-complex #triangulation #compact-manifolds
65
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Can a connected closed manifold strictly contain a closed manifold of the same dimension?

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#manifolds #compact-manifolds
572
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Does there exist a compact submanifold of $\mathbb{R}^3$ whose fundamental group is $\mathbb{Z}^3$?

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#algebraic-topology #homotopy-theory #fundamental-groups #submanifold #compact-manifolds
107
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Extending an embedding with trivial normal bundle

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#differential-geometry #differential-topology #smooth-manifolds #submanifold #compact-manifolds
102
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How to deal with boundary orientation in Exercise 16-5 from Lee's Introduction to Smooth Manifolds

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#integration #smooth-manifolds #stokes-theorem #manifolds-with-boundary #compact-manifolds
184
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Regularity of higher order elliptic problem on compact smooth manifolds with boundary

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#smooth-manifolds #regularity-theory-of-pdes #manifolds-with-boundary #compact-manifolds #elliptic-operators
358
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Subharmonic Functions on Closed Manifolds are Constant?

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#partial-differential-equations #laplacian #compact-manifolds
48
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Proof that a compact surface has a tangent plane orthogonal to position

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#differential-topology #vector-analysis #compact-manifolds

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