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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeAug 26th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexOne more item for the list of _[[Sullivan models -- examples]]_ <a href="https://ncatlab.org/nlab/revision/Sullivan+model+of+classifying+space/1">v1</a>, <a href="https://ncatlab.org/nlab/show/Sullivan+model+of+classifying+space">current</a>

   One more item for the list of Sullivan models – examples

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorTim_Porter
   • CommentTimeAug 27th 2020
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexThe title seems to me to read slightly strangely; perhaps 'Sullivan model of a classifying space' or `Sullivan model of the classifying space of a Lie group' might get around the problem.

   The title seems to me to read slightly strangely; perhaps ’Sullivan model of a classifying space’ or ‘Sullivan model of the classifying space of a Lie group’ might get around the problem.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeAug 27th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexSure. Had this as redirect, but changed title now. <a href="https://ncatlab.org/nlab/revision/diff/Sullivan+model+of+a+classifying+space/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/Sullivan+model+of+a+classifying+space/3">v3</a>, <a href="https://ncatlab.org/nlab/show/Sullivan+model+of+a+classifying+space">current</a>

   Sure. Had this as redirect, but changed title now.

   diff, v3, current

4. • CommentRowNumber4.
   • CommentAuthorperezl.alonso
   • CommentTime5 days ago
   • PermaLink
   Author: perezl.alonso
   Format: MarkdownItexSo this entry talks about a finite-dimensional simply connected compact Lie group. What does one do for higher smooth groups e.g. a [[string group]]?

   So this entry talks about a finite-dimensional simply connected compact Lie group. What does one do for higher smooth groups e.g. a string group?

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTime5 days ago
   • PermaLink
   Author: Urs
   Format: MarkdownItexThe assumptions listed are just those for which there are classical formulas for the rational cohomology of $B G$, as cited. For $B String$, the defining homotopy fiber sequence $$ B^3 \mathbb{Z} \longrightarrow B String \longrightarrow B Spin \overset{\tfrac{1}{2}p_1}{\longrightarrow} B^4 \mathbb{Z} $$ with its induced [[long exact sequence of homotopy groups]], implies that $B String$ has the same (rational) homotopy groups as $B Spin$ except the ones in degree 4. Since the algebra generators of a Sullivan model are these rationalized homotopy groups, this means that also the Sullivan models are the same except that the invariant polynomial which is the 1st Pontrjagin form disappears for $B String$.

   The assumptions listed are just those for which there are classical formulas for the rational cohomology of , as cited.

   For , the defining homotopy fiber sequence

   with its induced long exact sequence of homotopy groups, implies that has the same (rational) homotopy groups as except the ones in degree 4.

   Since the algebra generators of a Sullivan model are these rationalized homotopy groups, this means that also the Sullivan models are the same except that the invariant polynomial which is the 1st Pontrjagin form disappears for .