Loop space decompositions of (2 n- 2) -connected (4 n- 1) -dimensional Poincaré Duality complexes
Loop space decompositions of (2 n- 2) -connected (4 n- 1) -dimensional Poincaré Duality complexes
Beben and Wu showed that if M is a (2 n- 2) -connected (4 n- 1) -dimensional Poincaré Duality complex such that n≥ 3 and H2n(M; Z) consists only of odd torsion, then Ω M can be decomposed up to homotopy as a product of simpler, well-studied spaces. We use a result from Beben and Theriault (Doc Math 27:183-211, 2022) to greatly simplify and enhance Beben and Wu’s work and to extend it in various directions.
Loop space decomposition, Poincare duality space, Whitehead product
Huang, Ruizhi
86809c85-b4f2-4048-9894-c37cd234e12c
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
5 August 2022
Huang, Ruizhi
86809c85-b4f2-4048-9894-c37cd234e12c
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Huang, Ruizhi and Theriault, Stephen
(2022)
Loop space decompositions of (2 n- 2) -connected (4 n- 1) -dimensional Poincaré Duality complexes.
Research in the Mathematical Sciences, 9 (3), [53].
(doi:10.1007/s40687-022-00338-y).
Abstract
Beben and Wu showed that if M is a (2 n- 2) -connected (4 n- 1) -dimensional Poincaré Duality complex such that n≥ 3 and H2n(M; Z) consists only of odd torsion, then Ω M can be decomposed up to homotopy as a product of simpler, well-studied spaces. We use a result from Beben and Theriault (Doc Math 27:183-211, 2022) to greatly simplify and enhance Beben and Wu’s work and to extend it in various directions.
Text
torsion-manifold-revised
- Accepted Manuscript
More information
Accepted/In Press date: 9 June 2022
Published date: 5 August 2022
Additional Information:
Funding Information:
Research supported in part by the National Natural Science Foundation of China (Grant Nos. 11801544 and 11688101), the National Key R &D Program of China (No. 2021YFA1002300), the Youth Innovation Promotion Association of Chinese Academy Sciences, and the “Chen Jingrun” Future Star Program of AMSS.
Publisher Copyright:
© 2022, The Author(s).
Keywords:
Loop space decomposition, Poincare duality space, Whitehead product
Identifiers
Local EPrints ID: 467332
URI: http://eprints.soton.ac.uk/id/eprint/467332
ISSN: 2197-9847
PURE UUID: c0ac7edb-e9ed-4173-b91e-f6b32607cf6d
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Date deposited: 06 Jul 2022 16:59
Last modified: 18 Mar 2024 05:29
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Author:
Ruizhi Huang
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