Steenrod ∪i-products on Bredon - Illman cohomology

Grégory Ginot

doi:10.1016/j.topol.2004.04.001

Steenrod ∪_i-products on Bredon - Illman cohomology

Grégory Ginot

University Paris 13
ENS Paris-Saclay

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Let G be a topological group acting on a space X. We construct a family of Steenrod's ∪_i-product [Ann. of Math. (2) 48 (1947) 290] on the Bredon-Illman cochain complex of X [Quart. J. Math. Oxford Ser. (2) 47 (1996) 199]. As corollaries, we get the existence of Steenrod squares on Bredon-Illman cohomology with appropriate coefficients as well as the triviality of the Gerstenhaber bracket induced by the braces at the cochain level [G. Mukherjee, N. Pandey, Homotopy G-algebra structure on Bredon-Illman cochain complex, Preprint].

Original language	English
Pages (from-to)	241-248
Number of pages	8
Journal	Topology and its Applications
Volume	143
Issue number	1-3
DOIs	https://doi.org/10.1016/j.topol.2004.04.001
Publication status	Published - 28 Aug 2004
Externally published	Yes

Keywords

Bredon-Illman cohomology
Cup-products
Gerstenhaber algebras
Steenrod squares

Access to Document

10.1016/j.topol.2004.04.001

Cite this

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title = "Steenrod ∪i-products on Bredon - Illman cohomology",

abstract = "Let G be a topological group acting on a space X. We construct a family of Steenrod's ∪i-product [Ann. of Math. (2) 48 (1947) 290] on the Bredon-Illman cochain complex of X [Quart. J. Math. Oxford Ser. (2) 47 (1996) 199]. As corollaries, we get the existence of Steenrod squares on Bredon-Illman cohomology with appropriate coefficients as well as the triviality of the Gerstenhaber bracket induced by the braces at the cochain level [G. Mukherjee, N. Pandey, Homotopy G-algebra structure on Bredon-Illman cochain complex, Preprint].",

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language = "English",

volume = "143",

pages = "241--248",

journal = "Topology and its Applications",

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TY - JOUR

T1 - Steenrod ∪i-products on Bredon - Illman cohomology

AU - Ginot, Grégory

PY - 2004/8/28

Y1 - 2004/8/28

N2 - Let G be a topological group acting on a space X. We construct a family of Steenrod's ∪i-product [Ann. of Math. (2) 48 (1947) 290] on the Bredon-Illman cochain complex of X [Quart. J. Math. Oxford Ser. (2) 47 (1996) 199]. As corollaries, we get the existence of Steenrod squares on Bredon-Illman cohomology with appropriate coefficients as well as the triviality of the Gerstenhaber bracket induced by the braces at the cochain level [G. Mukherjee, N. Pandey, Homotopy G-algebra structure on Bredon-Illman cochain complex, Preprint].

AB - Let G be a topological group acting on a space X. We construct a family of Steenrod's ∪i-product [Ann. of Math. (2) 48 (1947) 290] on the Bredon-Illman cochain complex of X [Quart. J. Math. Oxford Ser. (2) 47 (1996) 199]. As corollaries, we get the existence of Steenrod squares on Bredon-Illman cohomology with appropriate coefficients as well as the triviality of the Gerstenhaber bracket induced by the braces at the cochain level [G. Mukherjee, N. Pandey, Homotopy G-algebra structure on Bredon-Illman cochain complex, Preprint].

KW - Bredon-Illman cohomology

KW - Cup-products

KW - Gerstenhaber algebras

KW - Steenrod squares

U2 - 10.1016/j.topol.2004.04.001

DO - 10.1016/j.topol.2004.04.001

M3 - Article

AN - SCOPUS:4243137173

SN - 0166-8641

VL - 143

SP - 241

EP - 248

JO - Topology and its Applications

JF - Topology and its Applications

IS - 1-3