Homology of spaces of regular loops in the sphere
Algebraic and Geometric Topology, Tome 9 (2009) no. 2, pp. 935-977
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In this paper we compute the singular homology of the space of immersions of the circle into the n–sphere. Equipped with the Chas–Sullivan loop product these homology groups are graded commutative algebras, which we also compute. We enrich Morse spectral sequences for fibrations of free loop spaces together with loop products. This offers some new computational tools for string topology.
Keywords:
free loop space, immersion space, string operation, Morse
theory, spectral sequence
Affiliations des auteurs :
Chataur, David 1 ; Le Borgne, Jean-François 1
@article{10_2140_agt_2009_9_935,
author = {Chataur, David and Le Borgne, Jean-Fran\c{c}ois},
title = {Homology of spaces of regular loops in the sphere},
journal = {Algebraic and Geometric Topology},
pages = {935--977},
publisher = {mathdoc},
volume = {9},
number = {2},
year = {2009},
doi = {10.2140/agt.2009.9.935},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2009.9.935/}
}
TY - JOUR AU - Chataur, David AU - Le Borgne, Jean-François TI - Homology of spaces of regular loops in the sphere JO - Algebraic and Geometric Topology PY - 2009 SP - 935 EP - 977 VL - 9 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2009.9.935/ DO - 10.2140/agt.2009.9.935 ID - 10_2140_agt_2009_9_935 ER -
%0 Journal Article %A Chataur, David %A Le Borgne, Jean-François %T Homology of spaces of regular loops in the sphere %J Algebraic and Geometric Topology %D 2009 %P 935-977 %V 9 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2009.9.935/ %R 10.2140/agt.2009.9.935 %F 10_2140_agt_2009_9_935
Chataur, David; Le Borgne, Jean-François. Homology of spaces of regular loops in the sphere. Algebraic and Geometric Topology, Tome 9 (2009) no. 2, pp. 935-977. doi: 10.2140/agt.2009.9.935
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