Geodesic
The classifying space of the 1+1 dimensional $G$-cobordism category
Homology, homotopy, and applications, Tome 25 (2023) no. 2, pp. 37-54.

Voir la notice de l'article provenant de la source International Press of Boston

For a finite group $G$, we define the $G$-cobordism category in dimension two. We show there is a one-to-one correspondence between the connected components of its classifying space and the abelianization of $G$. Also, we find an isomorphism of its fundamental group onto the direct sum $\mathbb{Z} \oplus \Omega^{SO}_{2} (BG)$, where $\Omega^{SO}_{2} (BG)$ is the free oriented $G$-bordism group in dimension two, and we study the classifying space of some important subcategories. We obtain the classifying space has the homotopy type of the product $G/[G,G] \times S^1 \times X^G$, where $\pi_1 (X^G) = \Omega^{SO}_{2} (BG)$. Finally, we present some results about the classification of $G$-topological quantum field theories in dimension two.
DOI : 10.4310/HHA.2023.v25.n2.a3
Classification : 55P91, 57R85
Keywords: cobordism category, classifying space, $G$-cobordism 
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     title = {The classifying space of the 1+1 dimensional $G$-cobordism category},
     journal = {Homology, homotopy, and applications},
     pages = {37--54},
     publisher = {mathdoc},
     volume = {25},
     number = {2},
     year = {2023},
     doi = {10.4310/HHA.2023.v25.n2.a3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2023.v25.n2.a3/}
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Carlos Segovia. The classifying space of the 1+1 dimensional $G$-cobordism category. Homology, homotopy, and applications, Tome 25 (2023) no. 2, pp. 37-54. doi : 10.4310/HHA.2023.v25.n2.a3. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2023.v25.n2.a3/

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