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The type of a torsion free finite loop space

Topology and Its Applications, 1991
In this paper we prove the following theorems: Theorem 1. If X is a two-torsion free finite loop space whose type consists of integers that are divisible by 4 and are less than 60, then X is of Lie type. Theorem 2.
James P Lin, Frank Williams
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On the Free Loop Space of Homogeneous Spaces

American Journal of Mathematics, 1987
This paper shows that if M is a compact simply connected homogeneous space which is not diffeomorhic to a symmetric space of rank one, then the Betti numbers with \({\mathbb{Z}}_ 2\)-coefficients of the free loop space of M are unbounded. As a corollary, the authors extend a result of Gromoll-Meyer to show that any Riemannian metric on M has infinitely
McCleary, John, Ziller, Wolfgang
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The free loop space and the algebraic k-theory of spaces

K-Theory, 1987
Let \(\Lambda(X)\) denote the free loop space of a space X, let \(\Sigma\) denote suspension, and \(Q=\Omega^{\infty}\Sigma^{\infty}\). Define \(B(X)=Q\Sigma (ES^ 1\times_{S^ 1} \Lambda (X))\), and \(\tilde B(X)=fibre(B(X)\to B(point))\). Let A(X) denote the algebraic K-theory of the space X, and \(\tilde A(X)=\text{fibre}(A(X)\to A(\text{point ...
Carlsson, G. E., Cohen, R. L., Goodwillie, T., Hsiang, W. C.   +3 more
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A model for the free loop space of a suspension

Lecture Notes in Mathematics, 1987
Ralph L Cohen, Cohen Ralph L
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Corrections to "On the Free Loop Space of Homogeneous Spaces"

American Journal of Mathematics, 1991
David Anick and Jan-Erik Roos have pointed out that Lemma 2 (the 'trick of Svarc') of [McC-ZI does not hold in the generality stated. The simplest counterexample is the manifold Sln. The key role played by this lemma in the proof of the main theorem of the paper requires that an alternative to the lemma be given and a re-examination of the details of ...
John McCleary, Wolfgang Ziller
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Morava K-Theory and the Free Loop Space

Proceedings of the American Mathematical Society, 1992
Summary: We generalize a result of Hopkins, Kuhn, and Ravenel relating the \(n\)th Morava \(K\)-theory of the free loop space of a classifying space of a finite group to the \((n+1)\)st Morava \(K\)-theory of the space. We show that the analogous result holds for any Eilenberg-Mac Lane space for a finite group.
McCleary, John, McLaughlin, Dennis A.
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Invariant Sobolev Calculus on the Free Loop Space

Acta Applicandae Mathematica, 1997
In this substantial and fundamental paper the differential calculus on the free loop space is studied. More precisely, a (scalar) Sobolev calculus invariant under the circle action is developed on the free loop space equipped with the Bismut/Høegh-Krohn measure which takes the role of the (otherwise absent) volume measure.
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Gaussian measures on free loop spaces

Russian Mathematical Surveys, 2001
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Free loopspaces and equivariant classifying spaces

Archiv der Mathematik, 2001
For \(\pi\) a discrete group, \(X\) a classifying space for \(\pi\), SO(2) the topological group of rotations of the plane about the origin and \({\mathcal C}_k\) the cyclic subgroup with \(k\) elements, \({\mathcal C}_k\subset \text{SO}(2)\), the author gives a group-theoretic description of the \({\mathcal C}_k\)-equivariant homotopy type of the path
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Basics on free loop spaces

2015
David Chataur, Alexandru Oancea
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