Homology, Homotopy and Applications

Volume 13 (2011)

Number 2

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

Pages: 43 – 62

DOI: http://dx.doi.org/10.4310/HHA.2011.v13.n2.a4

Author

Matthew S. Miller (Mathematics Department, Vassar College, Poughkeepsie, New York, U.S.A.)

Abstract

We study the algebraic topology of configuration spaces as interesting objects in their own right and with the goal of constructing invariants for topological manifolds. We calculate the complete Massey product structure for the universal cover of the space of two point configurations in a three-dimensional lens space. We then construct rational homotopy models for these spaces and calculate the rational homotopy groups.

Keywords

homology; homotopy; Massey product; lens space; configuration space

2010 Mathematics Subject Classification

55P62, 55S30, 57N65, 57N75

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