NOTES ON FLOER HOMOLOGY AND LOOP SPACE HOMOLOGY

2005 ◽  
pp. 75-108 ◽  
Author(s):  
ALBERTO ABBONDANDOLO ◽  
MATTHIAS SCHWARZ
Keyword(s):  
Loop Space ◽  
Floer Homology ◽  
Space Homology ◽  
Loop Space Homology

scholarly journals Continuation homomorphism in Rabinowitz Floer homology for symplectic deformations

2011 ◽  
Vol 151 (3) ◽  
pp. 471-502 ◽  
Author(s):  
YOUNGJIN BAE ◽  
URS FRAUENFELDER
Keyword(s):  
Exact Sequence ◽  
Isoperimetric Inequality ◽  
Short Exact Sequence ◽  
Loop Space ◽  
Floer Homology ◽  
Critical Value ◽  
Alternative Proof ◽  
Rabinowitz Floer Homology ◽  
Space Homology ◽  
Loop Space Homology

AbstractWill J. Merry computed Rabinowitz Floer homology above Mañé's critical value in terms of loop space homology in [14] by establishing an Abbondandolo–Schwarz short exact sequence. The purpose of this paper is to provide an alternative proof of Merry's result. We construct a continuation homomorphism for symplectic deformations which enables us to reduce the computation to the untwisted case. Our construction takes advantage of a special version of the isoperimetric inequality which above Mañé's critical value holds true.

Koszul A∞-algebras and free loop space homology

2019 ◽  
Vol 63 (1) ◽  
pp. 37-65
Author(s):  
Alexander Berglund ◽  
Kaj Börjeson
Keyword(s):  
Loop Space ◽  
Free Loop Space ◽  
Koszul Algebra ◽  
New Techniques ◽  
Space Homology ◽  
Loop Space Homology

AbstractWe introduce a notion of Koszul A∞-algebra that generalizes Priddy's notion of a Koszul algebra and we use it to construct small A∞-algebra models for Hochschild cochains. As an application, this yields new techniques for computing free loop space homology algebras of manifolds that are either formal or coformal (over a field or over the integers). We illustrate these techniques in two examples.

scholarly journals Loop space homology associated with the mod 2 Dickson invariants

2012 ◽  
Vol 24 (6) ◽  
Author(s):  
Ran Levi ◽  
Nora Seeliger
Keyword(s):  
Loop Space ◽  
Space Homology ◽  
Loop Space Homology

scholarly journals Torsion primes in loop space homology

Topology ◽  
2004 ◽  
Vol 43 (2) ◽  
pp. 493-496
Author(s):  
Y. Felix ◽  
S. Halperin ◽  
J.-C. Thomas
Keyword(s):  
Loop Space ◽  
Space Homology ◽  
Loop Space Homology

Loop Space Homology of Spaces of Small Category

1993 ◽  
Vol 338 (2) ◽  
pp. 711
Author(s):  
Yves Felix ◽  
Jean-Claude Thomas
Keyword(s):  
Loop Space ◽  
Small Category ◽  
Space Homology ◽  
Loop Space Homology

Multiplicity two actions and loop space homology

1993 ◽  
Vol 13 (1) ◽  
pp. 143-151 ◽  
Author(s):  
Gabriel P. Paternain
Keyword(s):  
Loop Space ◽  
Symmetry Groups ◽  
Compact Lie Groups ◽  
Field Coefficient ◽  
Topological Obstructions ◽  
Low Dimensional ◽  
Simply Connected ◽  
Hamiltonian Actions ◽  
Space Homology ◽  
Loop Space Homology

AbstractWe study Hamiltonian actions of compact Lie groups with low dimensional Marsden-Weinstein reduced spaces. We show that Hamiltonian systems with such symmetry groups have zero topological entropy and easily described dynamics. As a result we show that if the geodesic flow of a compact simply connected Riemannian manifold admits such a symmetry group, then the loop space homology of the manifold grows sub-exponentially with any field coefficient. Topological obstructions for collective complete integrability are thus obtained.

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