On the homotopy transfer of $A_\infty$ structures
Archivum mathematicum, Tome 53 (2017) no. 5, pp. 267-312 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The present article is devoted to the study of transfers for $A_\infty $ structures, their maps and homotopies, as developed in [7]. In particular, we supply the proofs of claims formulated therein and provide their extension by comparing them with the former approach based on the homological perturbation lemma.
The present article is devoted to the study of transfers for $A_\infty $ structures, their maps and homotopies, as developed in [7]. In particular, we supply the proofs of claims formulated therein and provide their extension by comparing them with the former approach based on the homological perturbation lemma.
DOI : 10.5817/AM2017-5-267
Classification : 18D10, 55S99
Keywords: $A_\infty $ structures; transfer; homological perturbation lemma
@article{10_5817_AM2017_5_267,
     author = {Kop\v{r}iva, Jakub},
     title = {On the homotopy transfer of $A_\infty$ structures},
     journal = {Archivum mathematicum},
     pages = {267--312},
     year = {2017},
     volume = {53},
     number = {5},
     doi = {10.5817/AM2017-5-267},
     mrnumber = {3746065},
     zbl = {06861558},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2017-5-267/}
}
TY  - JOUR
AU  - Kopřiva, Jakub
TI  - On the homotopy transfer of $A_\infty$ structures
JO  - Archivum mathematicum
PY  - 2017
SP  - 267
EP  - 312
VL  - 53
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.5817/AM2017-5-267/
DO  - 10.5817/AM2017-5-267
LA  - en
ID  - 10_5817_AM2017_5_267
ER  - 
%0 Journal Article
%A Kopřiva, Jakub
%T On the homotopy transfer of $A_\infty$ structures
%J Archivum mathematicum
%D 2017
%P 267-312
%V 53
%N 5
%U http://geodesic.mathdoc.fr/articles/10.5817/AM2017-5-267/
%R 10.5817/AM2017-5-267
%G en
%F 10_5817_AM2017_5_267
Kopřiva, Jakub. On the homotopy transfer of $A_\infty$ structures. Archivum mathematicum, Tome 53 (2017) no. 5, pp. 267-312. doi: 10.5817/AM2017-5-267

[1] Crainic, M.: On the perturbation lemma, and deformations. 2004, ArXiv preprint math.AT/0403266.

[2] Hatcher, A.: Algebraic topology. Cambridge University Press, Cambridge, New York, 2002. | MR | Zbl

[3] Huebschmann, J.: On the construction of $A_\infty $-structures. Georgian Math. J. 17 (1) (2010), 161–202. | MR | Zbl

[4] Keller, B.: Introduction to $A_\infty $ algebras and modules. Homology Homotopy Appl. 3 (1) (2001), 1–35. | MR

[5] Kontsevich, M., Soibelman, Y.: Homological mirror symmetry and torus fibrations, Symplectic geometry and mirror symmetry. (Seoul, 2000), World Sci. Publ., River Edge, NJ (2001), 203–263. | MR

[6] Lefèvre-Hasegawa, K.: Sur les $A_\infty $ catégories. Ph.D. thesis, Université Paris 7 – Denis Diderot, 2003.

[7] Markl, M.: Transferring $A_\infty $ (strongly homotopy associative) structures. Rend. Circ. Mat. Palermo (2) Suppl. (2006), no. 79, 139–151. | MR | Zbl

[8] Markl, M., Shnider, S., Stasheff, J.D.: Operads in Algebra, Topology and Physics. Mathematical Surveys and Monographs, American Mathematical Society, Providence, Rhode Island, 2002. | MR | Zbl

[9] Merkulov, S.: Strongly Homotopy Algebras of a Kähler Manifold. Internat. Math. Res. Notices (1999), no. 3, 153–164. | DOI

[10] Prouté, A.: $A_\infty $-structures: Modèles Minimaux de Baues-Lemaire et Kadeishvili et Homologie des Fibrations. Ph.D. thesis, Université Paris 7 – Denis Diderot, 1986.

[11] Weibel, C.A.: An introduction to homological algebra. Cambridge University Press, 1995. | Zbl

Cité par Sources :