The free loop space and the algebraic k-theory of spaces

K-Theory ◽  
1987 ◽  
Vol 1 (1) ◽  
pp. 53-82 ◽  
Author(s):  
G. E. Carlsson ◽  
R. L. Cohen ◽  
T. Goodwillie ◽  
W. c. Hsiang
Keyword(s):  
Loop Space ◽  
Free Loop Space ◽  
K Theory

scholarly journals Morava $K$-theory and the free loop space

1992 ◽  
Vol 114 (1) ◽  
pp. 243-243
Author(s):  
John McCleary ◽  
Dennis A. McLaughlin
Keyword(s):  
Loop Space ◽  
Free Loop Space ◽  
K Theory

Morava K-Theory and the Free Loop Space

1992 ◽  
Vol 114 (1) ◽  
pp. 243
Author(s):  
John McCleary ◽  
Dennis A. McLaughlin
Keyword(s):  
Loop Space ◽  
Free Loop Space ◽  
K Theory

scholarly journals On the K-theory of the loop space of a Lie group

1974 ◽  
Vol 76 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Francis Clarke
Keyword(s):  
Lie Group ◽  
Loop Space ◽  
Simple Structure ◽  
Homology Theory ◽  
Compact Lie Group ◽  
Classifying Space ◽  
K Theory ◽  
Simply Connected ◽  
Torsion Free ◽  
Multiplicative Structures

Let G be a simply connected, semi-simple, compact Lie group, let K* denote Z/2-graded, representable K-theory, and K* the corresponding homology theory. The K-theory of G and of its classifying space BG are well known, (8),(1). In contrast with ordinary cohomology, K*(G) and K*(BG) are torsion-free and have simple multiplicative structures. If ΩG denotes the space of loops on G, it seems natural to conjecture that K*(ΩG) should have, in some sense, a more simple structure than H*(ΩG).

scholarly journals On vector bundles for a Morse decomposition of $L\mathbb{C}\mathrm{P}^n$

2017 ◽  
Vol 121 (2) ◽  
pp. 186
Author(s):  
Iver Ottosen
Keyword(s):  
Loop Space ◽  
Vector Bundles ◽  
Morse Decomposition ◽  
Energy Integral ◽  
Chern Classes ◽  
Free Loop Space ◽  
Stiefel Manifolds ◽  
Mod P

We give a description of the negative bundles for the energy integral on the free loop space $L\mathbb{C}\mathrm{P}^n$ in terms of circle vector bundles over projective Stiefel manifolds. We compute the mod $p$ Chern classes of the associated homotopy orbit bundles.

scholarly journals On the geometry of free loop spaces

2002 ◽  
Vol 30 (1) ◽  
pp. 15-23 ◽  
Author(s):  
P. Manoharan
Keyword(s):  
Fundamental Form ◽  
Open Subset ◽  
Loop Space ◽  
Free Loop Space ◽  
Loop Spaces ◽  
Central Extensions ◽  
Christoffel Symbols

We verify the following three basic results on the free loop spaceLM. (1) We show that the set of all points, where the fundamental form onLMis nondegenerate, is an open subset. (2) The connections of a Fréchet bundle overLMcan be extended toS1-central extensions and, in particular, there exist natural connections on the string structures. (3) The notion of Christoffel symbols and the curvature are introduced onLMand they are described in terms of Christoffel symbols ofM.

Cyclic homology of a free loop space

1993 ◽  
Vol 21 (2) ◽  
pp. 575-582
Author(s):  
Andrea Solotar
Keyword(s):  
Loop Space ◽  
Cyclic Homology ◽  
Free Loop Space

scholarly journals Topological Hochschild homology of Thom spectra and the free loop space

2010 ◽  
Vol 14 (2) ◽  
pp. 1165-1242 ◽  
Author(s):  
Andrew J Blumberg ◽  
Ralph L Cohen ◽  
Christian Schlichtkrull
Keyword(s):  
Loop Space ◽  
Hochschild Homology ◽  
Free Loop Space ◽  
Thom Spectra ◽  
Topological Hochschild Homology
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