scholarly journals Rational homotopy models for two-point configuration spaces of lens spaces

2011 ◽  
Vol 13 (2) ◽  
pp. 43-62 ◽  
Author(s):  
Matthew S. Miller
Keyword(s):  
Configuration Spaces ◽  
Lens Spaces ◽  
Rational Homotopy ◽  
Point Configuration

scholarly journals Representation stability for homotopy groups of configuration spaces

2018 ◽  
Vol 2018 (737) ◽  
pp. 217-253 ◽  
Author(s):  
Alexander Kupers ◽  
Jeremy Miller
Keyword(s):  
General Theorem ◽  
Configuration Spaces ◽  
Homotopy Groups ◽  
Rational Homotopy ◽  
Cohomology Groups ◽  
Finitely Generated ◽  
Connected Manifold ◽  
Representation Stability ◽  
Gerstenhaber Algebras

AbstractWe prove that the dual rational homotopy groups of the configuration spaces of a 1-connected manifold of dimension at least 3 are uniformly representation stable in the sense of [6], and that their derived dual integral homotopy groups are finitely generated as{{\mathsf{FI}}}-modules in the sense of [4]. This is a consequence of a more general theorem relating properties of the cohomology groups of a 1-connected co-{{\mathsf{FI}}}-space to properties of its dual homotopy groups. We also discuss several other applications, including free Lie and Gerstenhaber algebras.

scholarly journals The rational homotopy type of configuration spaces of two points

2004 ◽  
Vol 54 (4) ◽  
pp. 1029-1052 ◽  
Author(s):  
Pascal Lambrechts ◽  
Don Stanley
Keyword(s):  
Homotopy Type ◽  
Configuration Spaces ◽  
Rational Homotopy ◽  
Rational Homotopy Type

scholarly journals Rational Models of the Complement of a Subpolyhedron in a Manifold with Boundary

2018 ◽  
Vol 70 (2) ◽  
pp. 265-293 ◽  
Author(s):  
Hector Cordova Bulens ◽  
Pascal Lambrechts ◽  
Don Stanley
Keyword(s):  
Configuration Space ◽  
Compact Manifold ◽  
Algebraic Model ◽  
Configuration Spaces ◽  
Rational Homotopy ◽  
Homotopy Invariance ◽  
Rational Models ◽  
Manifold With Boundary ◽  
Rational Homotopy Type ◽  
Simply Connected

AbstractLet W be a compact simply connected triangulated manifold with boundary and let K ⊂ W be a subpolyhedron. We construct an algebraic model of the rational homotopy type of W\K out of a model of the map of pairs (K, K⋂∂W) ↪ (W, ∂W) under some high codimension hypothesis.We deduce the rational homotopy invariance of the configuration space of two points in a compact manifold with boundary under 2-connectedness hypotheses. Also, we exhibit nice explicit models of these configuration spaces for a large class of compact manifolds.

A GEOMETRIC INTERPRETATION OF THE SELBERG INTEGRAL

2003 ◽  
Vol 18 (24) ◽  
pp. 4343-4359
Author(s):  
MASAAKI YOSHIDA
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Geometric Interpretation ◽  
Reciprocity Relation ◽  
Configuration Spaces ◽  
Topological Properties ◽  
Selberg Integral ◽  
Point Configuration ◽  
Conformal Field

A geometric interpretation of the reciprocity relation of the Selberg integral is given. Combinatorial topological properties of the point-configuration spaces are used. It has an application to the conformal field theory.

Isometry classes of 3 dimensional lens spaces

2002 ◽  
Vol 13 (7) ◽  
pp. 295-299
Author(s):  
Michel Cahen ◽  
Mohamed Chaibi
Keyword(s):  
Lens Spaces ◽  
3 Dimensional
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