User Marion

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15

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13

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6k

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How to explain the formula for the sum of a geometric series without calculus?

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9

12

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1

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4k

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$S^2=SO(3)/SO(2)$. Does this mean that $S^2 = SU(2)/U(1) $?

differential-geometry algebraic-topology lie-groups

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782

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differential-geometry riemannian-geometry hyperbolic-geometry

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107

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physics mathematical-physics vector-bundles principal-bundles gauge-theory

Jan 2 '18 at 13:24 Marion 2,005

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general-topology geometry education learning spheres

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general-topology functions algebraic-topology

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4

votes

0

answers

310

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differential-geometry algebraic-geometry holomorphic-bundles

Nov 21 '16 at 23:46 Marion 2,005

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4

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3

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abstract-algebra algebraic-geometry quotient-spaces

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differential-geometry manifolds spheres

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4

votes

1

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774

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If $\phi: M_1 \to M_2$ a diffeomorphism between diff. manifolds, prove that if $M_2$ is oriented then so is $M_1$

differential-geometry manifolds smooth-manifolds orientation

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4

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6

answers

1k

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algebra-precalculus

Feb 12 '15 at 22:27 Casey Chu 270

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3

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1

answer

277

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algebraic-geometry algebraic-topology sheaf-theory

Sep 10 '17 at 16:50 Eric Wofsey 276k

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3

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1

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163

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Why do we need the $S \otimes L^{1/2}$ bundle product to determine a $Spin_c$ structure?

differential-geometry differential-topology vector-bundles fiber-bundles spin-geometry

Apr 14 '17 at 17:34 Community♦ 1

2

3

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1

answer

395

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Confusion: line bundles over $\mathbb{P}^1$ and sheaves

algebraic-geometry complex-geometry sheaf-theory vector-bundles fiber-bundles

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2

3

votes

0

answers

118

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Natural line bundle over $\mathbb{P}^n$

algebraic-geometry sheaf-theory projective-geometry holomorphic-bundles

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3

votes

1

answer

374

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differential-geometry lie-groups symplectic-geometry

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71

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complex-analysis mathematical-physics contour-integration gauge-theory

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complex-analysis algebraic-geometry mathematical-physics schemes

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What exactly is a conifold for mathematicians?

algebraic-geometry differential-geometry complex-geometry

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0

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group-theory lie-groups mathematical-physics

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1

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371

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Oct 3 '16 at 11:28 Marion 2,005

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2

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1

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326

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106 Questions

How to explain the formula for the sum of a geometric series without calculus?

$S^2=SO(3)/SO(2)$. Does this mean that $S^2 = SU(2)/U(1) $?

Physicist trying to understand GIT quotient

$q$-series and modular forms

Parallel transport of a vector in hyperbolic space, specifically in $\mathbb{H}$

Abelian instantons for generic metric

How to explain to a school kid that on a sphere the shortest path between 2 points is given by a great circle?

Liouville's theorem and the Wronskian

Fundamental group of $\mathbb{R}^n\backslash \{0\}$

Circle to circle homotopic to the constant map?

When are two line bundles isomorphic?

What is the quotient space $\mathbb{C}[x,y,z]/(x^2+y^2)$?

Prove that the antipodal mapping is an isometry on $S^n$. Help understanding the proof.

If $\phi: M_1 \to M_2$ a diffeomorphism between diff. manifolds, prove that if $M_2$ is oriented then so is $M_1$

3 points lie in the same straight line. Then why is this formula valid?

Euler characteristic of a pair of sheaves $(E,F)$?

Why do we need the $S \otimes L^{1/2}$ bundle product to determine a $Spin_c$ structure?

Confusion: line bundles over $\mathbb{P}^1$ and sheaves

Natural line bundle over $\mathbb{P}^n$

Is the group of symplectomorphisms of a symplectic manifold the symplectic group?

Can I split this integral to a sum over three contours?

What exactly does the Hilbert scheme of points parametrize?

What exactly is a conifold for mathematicians?

What information can I immediately extract from a Dynkin diagram?

Levi-Civita help

Log Sum Exp trick confusion with probability distributions

What exactly is the diagonal subgroup of a group?

What information does a group extension Ext$^1(X,Y)$ convey?

How to write this product function in a compact way?

Is there a Mobius (infinite) cylinder?