| Title:
|
On the homotopy transfer of $A_\infty$ structures (English) |
| Author:
|
Kopřiva, Jakub |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
53 |
| Issue:
|
5 |
| Year:
|
2017 |
| Pages:
|
267-312 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
$A_\infty $ structures |
| Keyword:
|
transfer |
| Keyword:
|
homological perturbation lemma |
| MSC:
|
18D10 |
| MSC:
|
55S99 |
| idZBL:
|
Zbl 06861558 |
| idMR:
|
MR3746065 |
| DOI:
|
10.5817/AM2017-5-267 |
| . |
| Date available:
|
2018-01-03T14:48:31Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147021 |
| . |
| Reference:
|
[1] Crainic, M.: On the perturbation lemma, and deformations.2004, ArXiv preprint math.AT/0403266. |
| Reference:
|
[2] Hatcher, A.: Algebraic topology.Cambridge University Press, Cambridge, New York, 2002. Zbl 1044.55001, MR 1867354 |
| Reference:
|
[3] Huebschmann, J.: On the construction of $A_\infty $-structures.Georgian Math. J. 17 (1) (2010), 161–202. Zbl 1202.55007, MR 2640649 |
| Reference:
|
[4] Keller, B.: Introduction to $A_\infty $ algebras and modules.Homology Homotopy Appl. 3 (1) (2001), 1–35. MR 1905779 |
| Reference:
|
[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 1882331 |
| Reference:
|
[6] Lefèvre-Hasegawa, K.: Sur les $A_\infty $ catégories.Ph.D. thesis, Université Paris 7 – Denis Diderot, 2003. |
| Reference:
|
[7] Markl, M.: Transferring $A_\infty $ (strongly homotopy associative) structures.Rend. Circ. Mat. Palermo (2) Suppl. (2006), no. 79, 139–151. Zbl 1112.18007, MR 2287133 |
| Reference:
|
[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. Zbl 1017.18001, MR 1898414 |
| Reference:
|
[9] Merkulov, S.: Strongly Homotopy Algebras of a Kähler Manifold.Internat. Math. Res. Notices (1999), no. 3, 153–164. 10.1155/S1073792899000070 |
| Reference:
|
[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. |
| Reference:
|
[11] Weibel, C.A.: An introduction to homological algebra.Cambridge University Press, 1995. Zbl 0834.18001 |
| . |
