On the homotopy transfer of A structures

Jakub Kopřiva

Archivum Mathematicum (2017)

  • Volume: 053, Issue: 5, page 267-312
  • ISSN: 0044-8753

Abstract

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The present article is devoted to the study of transfers for A 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.

How to cite

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Kopřiva, Jakub. "On the homotopy transfer of $A_\infty $ structures." Archivum Mathematicum 053.5 (2017): 267-312. <http://eudml.org/doc/294838>.

@article{Kopřiva2017,
abstract = {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.},
author = {Kopřiva, Jakub},
journal = {Archivum Mathematicum},
keywords = {$A_\infty $ structures; transfer; homological perturbation lemma},
language = {eng},
number = {5},
pages = {267-312},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On the homotopy transfer of $A_\infty $ structures},
url = {http://eudml.org/doc/294838},
volume = {053},
year = {2017},
}

TY - JOUR
AU - Kopřiva, Jakub
TI - On the homotopy transfer of $A_\infty $ structures
JO - Archivum Mathematicum
PY - 2017
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 053
IS - 5
SP - 267
EP - 312
AB - 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.
LA - eng
KW - $A_\infty $ structures; transfer; homological perturbation lemma
UR - http://eudml.org/doc/294838
ER -

References

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  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. (2002) Zbl1044.55001MR1867354
  3. Huebschmann, J., On the construction of A -structures, Georgian Math. J. 17 (1) (2010), 161–202. (2010) Zbl1202.55007MR2640649
  4. Keller, B., Introduction to A algebras and modules, Homology Homotopy Appl. 3 (1) (2001), 1–35. (2001) MR1905779
  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. (2001) MR1882331
  6. Lefèvre-Hasegawa, K., Sur les A catégories, Ph.D. thesis, Université Paris 7 – Denis Diderot, 2003. (2003) 
  7. Markl, M., Transferring A (strongly homotopy associative) structures, Rend. Circ. Mat. Palermo (2) Suppl. (2006), no. 79, 139–151. (2006) Zbl1112.18007MR2287133
  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. (2002) Zbl1017.18001MR1898414
  9. Merkulov, S., 10.1155/S1073792899000070, Internat. Math. Res. Notices (1999), no. 3, 153–164. (1999) DOI10.1155/S1073792899000070
  10. Prouté, A., A -structures: Modèles Minimaux de Baues-Lemaire et Kadeishvili et Homologie des Fibrations, Ph.D. thesis, Université Paris 7 – Denis Diderot, 1986. (1986) 
  11. Weibel, C.A., An introduction to homological algebra, Cambridge University Press, 1995. (1995) Zbl0834.18001

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