Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
  
  
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorSamuel Adrian Antz
   • CommentTimeMar 10th 2024
   • PermaLink
   Author: Samuel Adrian Antz
   Format: MarkdownItexCreated page for [[BU(n)]], the [[classifying space]] of the [[unitary group]] U(n). (See [discussion on Stiefel-Whitney class](https://nforum.ncatlab.org/discussion/3300/stiefelwhitney-class).) There is still a lot to add though. <a href="https://ncatlab.org/nlab/revision/BU%28n%29/1">v1</a>, <a href="https://ncatlab.org/nlab/show/BU%28n%29">current</a>

   Created page for BU(n), the classifying space of the unitary group U(n). (See discussion on Stiefel-Whitney class.) There is still a lot to add though.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMar 11th 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexThere seems to have been a glitch in the last sentence ("limit" instead of "colimit" and a sudden appearance if $SU(n)$ instead of $\mathrm{U}(n)$). I have fixed it and added a link to *[[stable unitary group]]*. <a href="https://ncatlab.org/nlab/revision/diff/BU%28n%29/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/BU%28n%29/2">v2</a>, <a href="https://ncatlab.org/nlab/show/BU%28n%29">current</a>

   There seems to have been a glitch in the last sentence (“limit” instead of “colimit” and a sudden appearance if instead of ). I have fixed it and added a link to stable unitary group.

   diff, v2, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMar 11th 2024
   • (edited Mar 11th 2024)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded cross-link with *[[KU]]*. <a href="https://ncatlab.org/nlab/revision/diff/BU%28n%29/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/BU%28n%29/2">v2</a>, <a href="https://ncatlab.org/nlab/show/BU%28n%29">current</a>

   added cross-link with KU.

   diff, v2, current

4. • CommentRowNumber4.
   • CommentAuthorSamuel Adrian Antz
   • CommentTimeMar 12th 2024
   • (edited Mar 12th 2024)
   • PermaLink
   Author: Samuel Adrian Antz
   Format: MarkdownItexAdded the simplest classifying space $B U(1)\cong\mathbb{C}P^\infty$ and its classification of $U(1)$ [[principal bundles]]. (A section about the general classification will follow soon.) Also linked the Wikipedia page _[Classifying space for U(n)](https://en.wikipedia.org/wiki/Classifying_space_for_U(n))_. Edit: As a link including ")" can't be linked due to disrupting the <div>[....](....)</div> environment, I have created a redirect from "Classifying space for unitary group". <a href="https://ncatlab.org/nlab/revision/diff/BU%28n%29/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/BU%28n%29/3">v3</a>, <a href="https://ncatlab.org/nlab/show/BU%28n%29">current</a>

   Added the simplest classifying space and its classification of principal bundles. (A section about the general classification will follow soon.) Also linked the Wikipedia page Classifying space for U(n).

   Edit: As a link including “)” can’t be linked due to disrupting the

   [….](….)

   environment, I have created a redirect from “Classifying space for unitary group”.

   diff, v3, current

5. • CommentRowNumber5.
   • CommentAuthorSamuel Adrian Antz
   • CommentTimeMar 12th 2024
   • PermaLink
   Author: Samuel Adrian Antz
   Format: MarkdownItexAdded reference for definition in Milnor & Stasheff. Added connection to [[characteristic classes]]. (I plan to create the page for [[balanced product]] in the future.) Also linked pages of [[BSO(n)]] and [[BSU(n)]], which I will create either today or tomorrow. <a href="https://ncatlab.org/nlab/revision/diff/BU%28n%29/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/BU%28n%29/4">v4</a>, <a href="https://ncatlab.org/nlab/show/BU%28n%29">current</a>

   Added reference for definition in Milnor & Stasheff. Added connection to characteristic classes. (I plan to create the page for balanced product in the future.) Also linked pages of BSO(n) and BSU(n), which I will create either today or tomorrow.

   diff, v4, current