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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMay 20th 2020
   • (edited May 20th 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded this pointer on the [[homotopy groups]] of the [[embedded cobordism category]]: * [[Marcel Bökstedt]], [[Anne Marie Svane]], _A geometric interpretation of the homotopy groups of the cobordism category_, Algebr. Geom. Topol. 14 (2014) 1649-1676 ([arXiv:1208.3370](https://arxiv.org/abs/1208.3370)) * [[Marcel Bökstedt]], [[Johan Dupont]], [[Anne Marie Svane]], _Cobordism obstructions to independent vector fields_, Q. J. Math. 66 (2015), no. 1, 13-61 ([arXiv:1208.3542](https://arxiv.org/abs/1208.3542)) <a href="https://ncatlab.org/nlab/revision/diff/cobordism+category/19">diff</a>, <a href="https://ncatlab.org/nlab/revision/cobordism+category/19">v19</a>, <a href="https://ncatlab.org/nlab/show/cobordism+category">current</a>

   added this pointer on the homotopy groups of the embedded cobordism category:

   • Marcel Bökstedt, Anne Marie Svane, A geometric interpretation of the homotopy groups of the cobordism category, Algebr. Geom. Topol. 14 (2014) 1649-1676 (arXiv:1208.3370)

   • Marcel Bökstedt, Johan Dupont, Anne Marie Svane, Cobordism obstructions to independent vector fields, Q. J. Math. 66 (2015), no. 1, 13-61 (arXiv:1208.3542)

   diff, v19, current

2. • CommentRowNumber2.
   • CommentAuthorJosh
   • CommentTimeMay 6th 2023
   • PermaLink
   Author: Josh
   Format: TextThere aren't many examples given here (or that I could find in general). Aside from the usual cobordism category of manifolds, is there anything preventing pseudomanifolds, or more generally pure simplicial complexes, from forming a cobordism category?

   There aren't many examples given here (or that I could find in general). Aside from the usual cobordism category of manifolds, is there anything preventing pseudomanifolds, or more generally pure simplicial complexes, from forming a cobordism category?
3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMay 6th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexSome good answers to this question are given as answers to [MO:q/59677](https://mathoverflow.net/q/59677/381).

   Some good answers to this question are given as answers to MO:q/59677.

4. • CommentRowNumber4.
   • CommentAuthorperezl.alonso
   • CommentTimeAug 26th 2023
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   Author: perezl.alonso
   Format: MarkdownItexOut of curiosity, what does the [[category of presheaves]] of a [[cobordism category]] look like? Seems like it would provide curious extensions of [[functorial field theory|functorial field theories]].

   Out of curiosity, what does the category of presheaves of a cobordism category look like? Seems like it would provide curious extensions of functorial field theories.