On homotopy nilpotency of loop spaces of Moore spaces

On homotopy nilpotency of some suspended spaces

Proceedings of the International Geometry Center ◽

10.15673/tmgc.v14i3.2032 ◽

2021 ◽

Vol 14 (3) ◽

pp. 164-186

Author(s):

Marek Golasinski

Keyword(s):

Loop Spaces ◽

Moore Spaces

A homological criterium from [Golasiński, M., On homotopy nilpotency of loop spaces of Moore spaces, Canad. Math. Bull. (2021), 1–12] is applied to investigate the homotopy nilpotency of some suspended spaces. We investigate the homotopy nilpotency of the wedge sum and smash products of Moore spaces M (A, n) with n ≥ 1. The homotopy nilpotency of homological spheres are studied as well.

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James-Hopf Invariants, Anick’s Spaces, and the Double Loops on Odd Primary Moore Spaces

Canadian Mathematical Bulletin ◽

10.4153/cmb-2000-030-9 ◽

2000 ◽

Vol 43 (2) ◽

pp. 226-235

Author(s):

Joseph Neisendorfer

Keyword(s):

Homotopy Groups ◽

Dimensional Sphere ◽

Double Loop ◽

Loop Spaces ◽

Moore Space ◽

Moore Spaces ◽

Hopf Invariants

AbstractUsing spaces introduced by Anick, we construct a decomposition into indecomposable factors of the double loop spaces of odd primary Moore spaces when the powers of the primes are greater than the first power. If n is greater than 1, this implies that the odd primary part of all the homotopy groups of the 2n + 1 dimensional sphere lifts to a mod pr Moore space.

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Homological epimorphisms, homotopy epimorphisms and acyclic maps

Forum Mathematicum ◽

10.1515/forum-2019-0249 ◽

2020 ◽

Vol 32 (6) ◽

pp. 1395-1406

Author(s):

Joseph Chuang ◽

Andrey Lazarev

Keyword(s):

Wide Class ◽

Topological Spaces ◽

Loop Spaces ◽

Graded Algebras ◽

Differential Graded Algebras ◽

Algebraic Description ◽

Acyclic Map ◽

Induced Maps

AbstractWe show that the notions of homotopy epimorphism and homological epimorphism in the category of differential graded algebras are equivalent. As an application we obtain a characterization of acyclic maps of topological spaces in terms of induced maps of their chain algebras of based loop spaces. In the case of a universal acyclic map we obtain, for a wide class of spaces, an explicit algebraic description for these induced maps in terms of derived localization.

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Joint continuity of K h C-functions with values in moore spaces

Ukrainian Mathematical Journal ◽

10.1007/s11253-009-0170-8 ◽

2008 ◽

Vol 60 (11) ◽

pp. 1803-1812 ◽

Cited By ~ 2

Author(s):

V. K. Maslyuchenko ◽

V. V. Mykhailyuk ◽

O. I. Filipchuk

Keyword(s):

Joint Continuity ◽

Moore Spaces

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RATIONAL LOCAL SYSTEMS AND CONNECTED FINITE LOOP SPACES

Glasgow Mathematical Journal ◽

10.1017/s0017089520000658 ◽

2021 ◽

pp. 1-29

Author(s):

DREW HEARD

Keyword(s):

Lie Group ◽

Loop Space ◽

Algebraic Model ◽

Compact Lie Group ◽

Loop Spaces ◽

Local Systems ◽

Special Case ◽

Finite Loop ◽

Finite Loop Space

Abstract Greenlees has conjectured that the rational stable equivariant homotopy category of a compact Lie group always has an algebraic model. Based on this idea, we show that the category of rational local systems on a connected finite loop space always has a simple algebraic model. When the loop space arises from a connected compact Lie group, this recovers a special case of a result of Pol and Williamson about rational cofree G-spectra. More generally, we show that if K is a closed subgroup of a compact Lie group G such that the Weyl group W G K is connected, then a certain category of rational G-spectra “at K” has an algebraic model. For example, when K is the trivial group, this is just the category of rational cofree G-spectra, and this recovers the aforementioned result. Throughout, we pay careful attention to the role of torsion and complete categories.

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