scholarly journals Topological coHochschild homology and the homology of free loop spaces

2022 ◽  
Author(s):  
Anna Marie Bohmann ◽  
Teena Gerhardt ◽  
Brooke Shipley
Keyword(s):  
Loop Spaces

scholarly journals Homological epimorphisms, homotopy epimorphisms and acyclic maps

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.

scholarly journals RATIONAL LOCAL SYSTEMS AND CONNECTED FINITE LOOP SPACES

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.

scholarly journals Monoid of self-equivalences and free loop spaces

2003 ◽  
Vol 132 (1) ◽  
pp. 305-312 ◽  
Author(s):  
Yves Félix ◽  
Jean-Claude Thomas
Keyword(s):  
Loop Spaces

Dirichlet operators on loop spaces: Essential self-adjointness and log-Sobolev inequality

1997 ◽  
Vol 38 (6) ◽  
pp. 3321-3346 ◽  
Author(s):  
Yong Moon Park ◽  
Hyun Jae Yoo
Keyword(s):  
Sobolev Inequality ◽  
Loop Spaces ◽  
Dirichlet Operators

scholarly journals On the homotopy-commutativity of loop-spaces and suspensions

Topology ◽  
1962 ◽  
Vol 1 (2) ◽  
pp. 133-141 ◽  
Author(s):  
T. Ganea ◽  
P.J. Hilton ◽  
F.P. Peterson
Keyword(s):  
Loop Spaces

scholarly journals Small loop spaces

2010 ◽  
Vol 157 (2) ◽  
pp. 451-455 ◽  
Author(s):  
Žiga Virk
Keyword(s):  
Loop Spaces ◽  
Small Loop

scholarly journals Differential forms on loop spaces and the cyclic bar complex

Topology ◽  
1991 ◽  
Vol 30 (3) ◽  
pp. 339-371 ◽  
Author(s):  
Ezra Getzler ◽  
John D.S. Jones ◽  
Scott Petrack
Keyword(s):  
Differential Forms ◽  
Loop Spaces

Loop spaces, cyclic homology and the Chern character

1989 ◽  
pp. 95-108
Author(s):  
E. Getzler ◽  
J.D.S. Jones ◽  
S.B. Petrack
Keyword(s):  
Chern Character ◽  
Cyclic Homology ◽  
Loop Spaces
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