List questions from spin-geometry

Published on 26 Mar 2026 - 4:31

91

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How to understand the spin structures on $T^d$ and $\mathbb{RP}^d$

Published on 01 Dec 2020 - 16:33

83

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Triangulable Spin 5-manifolds but do not admit any smooth structure

Published on 07 Dec 2020 - 15:41

142

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Why Spin(V) is a connected group?

Published on 20 Dec 2020 - 16:30

50

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Can spinors be generalized from $\mathbb{Z}_2$ to arbitrary polyhedral symmetry groups via topological gluing?

Published on 25 Dec 2020 - 22:27

1.5k

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What makes spinors mysterious?

Published on 26 Dec 2020 - 0:16

100

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Lie algebra of SO(V) is isomorphic to spin(V)

Published on 26 Dec 2020 - 23:57

269

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Demonstrate $\mathrm{Spin}(3, 3) = \mathrm{SL}(4, R)$

Published on 09 Jan 2021 - 3:34

118

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Unimportance of the metric for spin structures

Published on 01 Feb 2021 - 12:30

55

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If the bundle of orthonormal frames has a continuos/smooth global section will the bundle of spin frames also have one?

Published on 02 Feb 2021 - 12:54

45

Views

The maximal (special) unitary subgroup contained in the Spin group: $Spin(2N)\supset U(N) \supset SU(N) ?$

Published on 26 Mar 2026 - 4:38

47

Views

Isomorphism of representation spaces

Published on 16 Mar 2021 - 21:34

115

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Construction of $C\ell(V,q)$ for a quadratic space $(V,q)$ and proving an injection $V\hookrightarrow C\ell(V,q)$ exists.

Published on 31 Mar 2021 - 8:29

29

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Why these are representations of ${\rm Spin}(D)$ and not ${\rm SO}(D)$?

Published on 04 Apr 2021 - 19:15

108

Views

Classification of $\operatorname{spin}^c$ structures

Published on 26 Mar 2026 - 9:49

List Question

Quadratic enhancements of the intersection form and spin structures

How to understand the spin structures on $T^d$ and $\mathbb{RP}^d$

Triangulable Spin 5-manifolds but do not admit any smooth structure

Why Spin(V) is a connected group?

Can spinors be generalized from $\mathbb{Z}_2$ to arbitrary polyhedral symmetry groups via topological gluing?

What makes spinors mysterious?

Lie algebra of SO(V) is isomorphic to spin(V)

Demonstrate $\mathrm{Spin}(3, 3) = \mathrm{SL}(4, R)$

Unimportance of the metric for spin structures

If the bundle of orthonormal frames has a continuos/smooth global section will the bundle of spin frames also have one?

The maximal (special) unitary subgroup contained in the Spin group: $Spin(2N)\supset U(N) \supset SU(N) ?$

Isomorphism of representation spaces

Construction of $C\ell(V,q)$ for a quadratic space $(V,q)$ and proving an injection $V\hookrightarrow C\ell(V,q)$ exists.

Why these are representations of ${\rm Spin}(D)$ and not ${\rm SO}(D)$?

Classification of $\operatorname{spin}^c$ structures

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