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Loop spaces of configuration spaces and finite type
invariants
Toshitake Kohno
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Geometry & Topology Monographs 4
(2002) 143–160
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Abstract
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The total homology of the loop space of the configuration space of
ordered distinct n points in Rm has a structure
of a Hopf algebra defined by the 4–term relations if m≥3.
We describe a relation of between the cohomology of this loop space and
the set of finite type invariants for the pure braid group with n strands.
Based on this we give expressions of certain link invariants as integrals
over cycles of the above loop space.
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Keywords
loop space, configuration space, finite
type invariants, braid group, iterated integral
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Mathematical Subject Classification
Primary: 55P35
Secondary: 20F36, 57M27
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Publication
Received: 19 December 2001
Revised: 9 April 2002
Accepted: 22 July 2002
Published: 19 September 2002
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