# Homotopy orbits of free loop spaces

Fundamenta Mathematicae (1999)

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

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topBökstedt, 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

top- [Loday] J.-L. Loday, Cyclic Homology, Grundlehren Math. Wiss. 301, Springer, 1992.
- [Madsen] I. Madsen, Algebraic K-theory and traces, in: Current Developments in Mathematics, International Press, Boston, 1995, 191-321. Zbl0876.55004
- [Milgram] R. J. Milgram, Unstable Homotopy from the Stable Point of View, Lecture Notes in Math. 368, Springer, 1974. Zbl0274.55015
- [Ottosen] I. Ottosen, Higher cyclic reduced powers, J. Pure Appl. Algebra, to appear.
- [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
- [Smith81] L. Smith, On the characteristic zero cohomology of the free loop space, Amer. J. Math. 103 (1981), 887-910. Zbl0475.55004
- [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
- [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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