Publicado

2022-05-18

E-infinity coalgebra structure on chain complexes with integer coefficients

E-infinito coalgebra estructura en complejos de cadenas con coeficientes enteros

DOI:

https://doi.org/10.15446/recolma.v55n2.102690

Palabras clave:

Operad theory, Chain complexes, E-coalgebras, Barrat-Eccles operad (en)
Teoría de operads, complejos de cadenas, E-coalgebras, operad de Barrat-Eccles (es)

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Autores/as

  • Jesús Sánchez-Guevara Universidad de Costa Rica

The aim of this paper is to construct an E-operad inducing an E-coalgebra structure on chain complexes with integer coefficients, which is an alternative description to the E-coalgebra by the Barrat-Eccles operad.

El objetivo de este artículo es construir un E-operad que induce una estructura de E-coalgebra en los complejos de cadenas con coeficientes enteros. Esta construcción produce una descripción alternativa a la E-coalgebra del operad de Barrat-Eccles.

Referencias

M. G. Barratt and P. J. Eccles, T+-structures-I: a free group functor for stable homotopy theory, Topology 13 (1974), no. 1, 25-45. DOI: https://doi.org/10.1016/0040-9383(74)90036-6

C. Berger and B. Fresse, Combinatorial operad actions on cochains, Mathematical Proceedings of the Cambridge Philosophical Society 137 (2004), 135-174. DOI: https://doi.org/10.1017/S0305004103007138

C. Berger and I. Moerdijk, Resolution of coloured operads and rectification of homotopy algebras, Contemporary mathematics 431 (2007), 31-58. DOI: https://doi.org/10.1090/conm/431/08265

J. M. Boardman and R. M. Vogt, Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Mathematics, Springer Berlin Heidelberg, 1973. DOI: https://doi.org/10.1007/BFb0068547

M. Dehling and B. Vallette, Symmetric homotopy theory for operads, ArXiv e-prints (2015).

V. Ginzburg and M. Kapranov, Koszul duality for operads, Duke Math. J. 76 (1994), no. 1, 203-272. DOI: https://doi.org/10.1215/S0012-7094-94-07608-4

A. Prouté, Sur la transformation d'Eilenberg-Maclane, C. R. Acad. Sc. Paris 297 (1983), 193-194.

A. Prouté, Sur la diagonal d'Alexander-Whitney, C. R. Acad. Sc. Paris 299 (1984), 391-392.

J. Sánchez-Guevara, About L-algebras, Ph.D. thesis, Université Paris VII, Paris, 2016.

J. R. Smith, Iterating the cobar construction, American Mathematical Society: Memoirs of the American Mathematical Society, no. 524, American Mathematical Society, 1994. DOI: https://doi.org/10.1090/memo/0524

Cómo citar

APA

Sánchez-Guevara, J. . (2022). E-infinity coalgebra structure on chain complexes with integer coefficients. Revista Colombiana de Matemáticas, 55(2), 197–203. https://doi.org/10.15446/recolma.v55n2.102690

ACM

[1]
Sánchez-Guevara, J. 2022. E-infinity coalgebra structure on chain complexes with integer coefficients. Revista Colombiana de Matemáticas. 55, 2 (may 2022), 197–203. DOI:https://doi.org/10.15446/recolma.v55n2.102690.

ACS

(1)
Sánchez-Guevara, J. . E-infinity coalgebra structure on chain complexes with integer coefficients. rev.colomb.mat 2022, 55, 197-203.

ABNT

SÁNCHEZ-GUEVARA, J. . E-infinity coalgebra structure on chain complexes with integer coefficients. Revista Colombiana de Matemáticas, [S. l.], v. 55, n. 2, p. 197–203, 2022. DOI: 10.15446/recolma.v55n2.102690. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/102690. Acesso em: 10 jul. 2024.

Chicago

Sánchez-Guevara, Jesús. 2022. «E-infinity coalgebra structure on chain complexes with integer coefficients». Revista Colombiana De Matemáticas 55 (2):197-203. https://doi.org/10.15446/recolma.v55n2.102690.

Harvard

Sánchez-Guevara, J. . (2022) «E-infinity coalgebra structure on chain complexes with integer coefficients», Revista Colombiana de Matemáticas, 55(2), pp. 197–203. doi: 10.15446/recolma.v55n2.102690.

IEEE

[1]
J. . Sánchez-Guevara, «E-infinity coalgebra structure on chain complexes with integer coefficients», rev.colomb.mat, vol. 55, n.º 2, pp. 197–203, may 2022.

MLA

Sánchez-Guevara, J. . «E-infinity coalgebra structure on chain complexes with integer coefficients». Revista Colombiana de Matemáticas, vol. 55, n.º 2, mayo de 2022, pp. 197-03, doi:10.15446/recolma.v55n2.102690.

Turabian

Sánchez-Guevara, Jesús. «E-infinity coalgebra structure on chain complexes with integer coefficients». Revista Colombiana de Matemáticas 55, no. 2 (mayo 18, 2022): 197–203. Accedido julio 10, 2024. https://revistas.unal.edu.co/index.php/recolma/article/view/102690.

Vancouver

1.
Sánchez-Guevara J. E-infinity coalgebra structure on chain complexes with integer coefficients. rev.colomb.mat [Internet]. 18 de mayo de 2022 [citado 10 de julio de 2024];55(2):197-203. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/102690

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