Homotopy operations and rational homotopy type

David Blanc

doi:10.1007/978-3-0348-7863-0_4

Homotopy operations and rational homotopy type

David Blanc

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In [HS] and [F1] Halperin, Stasheff, and Félix showed how an inductively-defined sequence of elements in the cohomology of a graded commutative algebra over the rationals can be used to distinguish among the homotopy types of all possible realizations, thus providing a collection of algebraic invariants for distinguishing among rational homotopy types of spaces. There is also a dual version, in the setting of graded Lie algebras (see [O]).

Original language	English
Title of host publication	Categorical Decomposition Techniques in Algebraic Topology
Subtitle of host publication	International Conference in Algebraic Topology, Isle of Skye, Scotland, June 2001
Editors	G. Z. Arone, J. R. Hubbuck, R. Levi, M. S. Weiss
Place of Publication	Basel
Publisher	Birkhauser
Chapter	4
Pages	47-75
Number of pages	33
ISBN (Electronic)	978-3-0348-7863-0
ISBN (Print)	978-3-0348-9601-6
DOIs	https://doi.org/10.1007/978-3-0348-7863-0_4
State	Published - 2004

Publication series

Name	Progress in Mathematics
Volume	215
ISSN (Print)	0743-1643
ISSN (Electronic)	2296-505X

Keywords

math.AT
55P62; 55Q35, 55P15,18G50

Access to Document

10.1007/978-3-0348-7863-0_4

0410075v1

Cite this

Blanc, D. (2004). Homotopy operations and rational homotopy type. In G. Z. Arone, J. R. Hubbuck, R. Levi, & M. S. Weiss (Eds.), Categorical Decomposition Techniques in Algebraic Topology: International Conference in Algebraic Topology, Isle of Skye, Scotland, June 2001 (pp. 47-75). (Progress in Mathematics; Vol. 215). Birkhauser. https://doi.org/10.1007/978-3-0348-7863-0_4

@inproceedings{7b13dc12743b44a490312136c106eb72,

title = "Homotopy operations and rational homotopy type",

abstract = "In [HS] and [F1] Halperin, Stasheff, and F{\'e}lix showed how an inductively-defined sequence of elements in the cohomology of a graded commutative algebra over the rationals can be used to distinguish among the homotopy types of all possible realizations, thus providing a collection of algebraic invariants for distinguishing among rational homotopy types of spaces. There is also a dual version, in the setting of graded Lie algebras (see [O]).",

keywords = "math.AT, 55P62; 55Q35, 55P15,18G50",

author = "David Blanc",

year = "2004",

doi = "10.1007/978-3-0348-7863-0_4",

language = "English",

isbn = "978-3-0348-9601-6",

series = "Progress in Mathematics",

publisher = "Birkhauser",

pages = "47--75",

editor = "Arone, {G. Z.} and Hubbuck, {J. R.} and R. Levi and Weiss, {M. S.}",

booktitle = "Categorical Decomposition Techniques in Algebraic Topology",

address = "Switzerland",

}

Homotopy operations and rational homotopy type. / Blanc, David.
Categorical Decomposition Techniques in Algebraic Topology: International Conference in Algebraic Topology, Isle of Skye, Scotland, June 2001. ed. / G. Z. Arone; J. R. Hubbuck; R. Levi; M. S. Weiss. Basel: Birkhauser, 2004. p. 47-75 (Progress in Mathematics; Vol. 215).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Homotopy operations and rational homotopy type

AU - Blanc, David

PY - 2004

Y1 - 2004

N2 - In [HS] and [F1] Halperin, Stasheff, and Félix showed how an inductively-defined sequence of elements in the cohomology of a graded commutative algebra over the rationals can be used to distinguish among the homotopy types of all possible realizations, thus providing a collection of algebraic invariants for distinguishing among rational homotopy types of spaces. There is also a dual version, in the setting of graded Lie algebras (see [O]).

AB - In [HS] and [F1] Halperin, Stasheff, and Félix showed how an inductively-defined sequence of elements in the cohomology of a graded commutative algebra over the rationals can be used to distinguish among the homotopy types of all possible realizations, thus providing a collection of algebraic invariants for distinguishing among rational homotopy types of spaces. There is also a dual version, in the setting of graded Lie algebras (see [O]).

KW - math.AT

KW - 55P62; 55Q35, 55P15,18G50

U2 - 10.1007/978-3-0348-7863-0_4

DO - 10.1007/978-3-0348-7863-0_4

M3 - Conference contribution

SN - 978-3-0348-9601-6

T3 - Progress in Mathematics

SP - 47

EP - 75

BT - Categorical Decomposition Techniques in Algebraic Topology

A2 - Arone, G. Z.

A2 - Hubbuck, J. R.

A2 - Levi, R.

A2 - Weiss, M. S.

PB - Birkhauser

CY - Basel

ER -

Homotopy operations and rational homotopy type

Abstract

Publication series

Keywords

Access to Document

Fingerprint

Cite this