Homotopy orbits of free loop spaces

Marcel Bökstedt; Iver Ottosen

Fundamenta Mathematicae (1999)

  • Volume: 162, Issue: 3, page 251-275
  • ISSN: 0016-2736

Abstract

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Let X be a space with free loop space ΛX and mod two cohomology R = H*X. We construct functors Ω λ ( R ) and ℓ(R) together with algebra homomorphisms e : Ω λ ( R ) → H * ( Λ X ) and ψ : ℓ ( R ) → H * ( E S 1 × S 1 Λ X ) . When X is 1-connected and R is a symmetric algebra we show that these are isomorphisms.

How to cite

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Bökstedt, Marcel, and Ottosen, Iver. "Homotopy orbits of free loop spaces." Fundamenta Mathematicae 162.3 (1999): 251-275. <http://eudml.org/doc/212423>.

@article{Bökstedt1999,
abstract = {Let X be a space with free loop space ΛX and mod two cohomology R = H*X. We construct functors $Ω_λ(R)$ and ℓ(R) together with algebra homomorphisms $e: Ω_λ(R) → H*(ΛX)$ and $ψ: ℓ(R) → H*(ES^1×_\{S^1\}ΛX)$. When X is 1-connected and R is a symmetric algebra we show that these are isomorphisms.},
author = {Bökstedt, Marcel, Ottosen, Iver},
journal = {Fundamenta Mathematicae},
keywords = {free loop space; homotopy orbit},
language = {eng},
number = {3},
pages = {251-275},
title = {Homotopy orbits of free loop spaces},
url = {http://eudml.org/doc/212423},
volume = {162},
year = {1999},
}

TY - JOUR
AU - Bökstedt, Marcel
AU - Ottosen, Iver
TI - Homotopy orbits of free loop spaces
JO - Fundamenta Mathematicae
PY - 1999
VL - 162
IS - 3
SP - 251
EP - 275
AB - Let X be a space with free loop space ΛX and mod two cohomology R = H*X. We construct functors $Ω_λ(R)$ and ℓ(R) together with algebra homomorphisms $e: Ω_λ(R) → H*(ΛX)$ and $ψ: ℓ(R) → H*(ES^1×_{S^1}ΛX)$. When X is 1-connected and R is a symmetric algebra we show that these are isomorphisms.
LA - eng
KW - free loop space; homotopy orbit
UR - http://eudml.org/doc/212423
ER -

References

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  1. [Loday] J.-L. Loday, Cyclic Homology, Grundlehren Math. Wiss. 301, Springer, 1992. 
  2. [Madsen] I. Madsen, Algebraic K-theory and traces, in: Current Developments in Mathematics, International Press, Boston, 1995, 191-321. Zbl0876.55004
  3. [Milgram] R. J. Milgram, Unstable Homotopy from the Stable Point of View, Lecture Notes in Math. 368, Springer, 1974. Zbl0274.55015
  4. [Ottosen] I. Ottosen, Higher cyclic reduced powers, J. Pure Appl. Algebra, to appear. 
  5. [Schwartz] L. Schwartz, Unstable Modules over the Steenrod Algebra and Sullivan's Fixed Point Set Conjecture, Chicago Lectures in Mathematics, Univ. of Chicago Press, 1994. Zbl0871.55001
  6. [Smith81] L. Smith, On the characteristic zero cohomology of the free loop space, Amer. J. Math. 103 (1981), 887-910. Zbl0475.55004
  7. [Smith84] L. Smith, The Eilenberg-Moore spectral sequence and the mod 2 cohomology of certain free loop spaces, Illinois J. Math. 28 (1984), 516-522. Zbl0538.57025
  8. [St-Ep] N. E. Steenrod and D. B. A. Epstein, Cohomology Operations, Ann. of Math. Stud. 50, Princeton Univ. Press, 1962. 

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