(Co)homology self-closeness numbers of simply-connected spaces

2021 ◽  
Vol 23 (1) ◽  
pp. 1-16
Author(s):  
Pengcheng Li
Keyword(s):  
Simply Connected ◽  
Connected Spaces

The group of homotopy self-equivalences of non-simply-connected spaces using Postnikov decompositions II

1992 ◽  
Vol 122 (1-2) ◽  
pp. 127-135 ◽  
Author(s):  
John W. Rutter
Keyword(s):  
Group Extension ◽  
Equivalence Classes ◽  
Homotopy Groups ◽  
Geometric Proof ◽  
Homotopy Equivalence ◽  
Connected Space ◽  
Abelian Kernel ◽  
Simply Connected ◽  
Extension Sequence ◽  
Connected Spaces

SynopsisWe give here an abelian kernel (central) group extension sequence for calculating, for a non-simply-connected space X, the group of pointed self-homotopy-equivalence classes . This group extension sequence gives in terms of , where Xn is the nth stage of a Postnikov decomposition, and, in particular, determines up to extension for non-simplyconnected spaces X having at most two non-trivial homotopy groups in dimensions 1 and n. We give a simple geometric proof that the sequence splits in the case where is the generalised Eilenberg–McLane space corresponding to the action ϕ: π1 → aut πn, and give some information about the class of the extension in the general case.

scholarly journals Goodwillie Approximations to Higher Categories

2021 ◽  
Vol 272 (1333) ◽  
Author(s):  
Gijs Heuts
Keyword(s):  
Homotopy Theory ◽  
Symmetric Groups ◽  
Homotopy Groups ◽  
Rational Homotopy Theory ◽  
Rational Homotopy ◽  
Content Type ◽  
Simply Connected ◽  
Derivatives Of ◽  
Connected Spaces

We construct a Goodwillie tower of categories which interpolates between the category of pointed spaces and the category of spectra. This tower of categories refines the Goodwillie tower of the identity functor in a precise sense. More generally, we construct such a tower for a large class of ∞ \infty -categories C \mathcal {C} and classify such Goodwillie towers in terms of the derivatives of the identity functor of C \mathcal {C} . As a particular application we show how this provides a model for the homotopy theory of simply-connected spaces in terms of coalgebras in spectra with Tate diagonals. Our classification of Goodwillie towers simplifies considerably in settings where the Tate cohomology of the symmetric groups vanishes. As an example we apply our methods to rational homotopy theory. Another application identifies the homotopy theory of p p -local spaces with homotopy groups in a certain finite range with the homotopy theory of certain algebras over Ching’s spectral version of the Lie operad. This is a close analogue of Quillen’s results on rational homotopy.

scholarly journals Multi-Phases in Gauge Theories on Non-Simply Connected Spaces

2002 ◽  
Vol 107 (6) ◽  
pp. 1191-1200 ◽  
Author(s):  
H. Hatanaka ◽  
K. Ohnishi ◽  
M. Sakamoto ◽  
K. Takenaga
Keyword(s):  
Gauge Theories ◽  
Simply Connected ◽  
Connected Spaces

scholarly journals On semilocally simply connected spaces

2011 ◽  
Vol 158 (3) ◽  
pp. 397-408 ◽  
Author(s):  
Hanspeter Fischer ◽  
Dušan Repovš ◽  
Žiga Virk ◽  
Andreas Zastrow
Keyword(s):  
Simply Connected ◽  
Connected Spaces

scholarly journals Co-H-Spaces and Almost Localization

2014 ◽  
Vol 58 (2) ◽  
pp. 323-332
Author(s):  
Cristina Costoya ◽  
Norio Iwase
Keyword(s):  
Universal Covering ◽  
Connected Space ◽  
Converse Statement ◽  
Simply Connected ◽  
Connected Spaces

AbstractApart from simply connected spaces, a non-simply connected co-H-space is a typical example of a space X with a coaction of Bπ1 (X) along rX: X → Bπ1 (X), the classifying map of the universal covering. If such a space X is actually a co-H-space, then the fibrewise p-localization of rX (or the ‘almost’ p-localization of X) is a fibrewise co-H-space (or an ‘almost’ co-H-space, respectively) for every prime p. In this paper, we show that the converse statement is true, i.e. for a non-simply connected space X with a coaction of Bπ1 (X) along rX, X is a co-H-space if, for every prime p, the almost p-localization of X is an almost co-H-space.

scholarly journals Simply connected spaces

1951 ◽  
Vol 38 ◽  
pp. 179-203 ◽  
Author(s):  
Tudor Ganea
Keyword(s):  
Simply Connected ◽  
Connected Spaces
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