Homology of moduli spaces of linkages in high-dimensional Euclidean space

Schütz, Dirk

doi:10.2140/agt.2013.13.1183

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Homology of moduli spaces of linkages in high-dimensional Euclidean space

Dirk Schütz

Algebraic & Geometric Topology 13 (2013) 1183–1224

DOI: 10.2140/agt.2013.13.1183

Abstract

We study the topology of moduli spaces of closed linkages in $ℝ^{d}$ depending on a length vector $ℓ \in ℝ^{n}$ . In particular, we use equivariant Morse theory to obtain information on the homology groups of these spaces, which works best for odd $d$ . In the case $d = 5$ we calculate the Poincaré polynomial in terms of combinatorial information encoded in the length vector.

Keywords

moduli spaces, linkages, homology

Mathematical Subject Classification 2010

Primary: 58D29

Secondary: 55R80, 57R70

References

Publication

Received: 19 July 2012

Revised: 21 December 2012

Accepted: 23 December 2012

Published: 18 April 2013

Authors

Dirk Schütz
Department of Mathematical Sciences University of Durham South Road Durham DH1 3LE UK
http://www.maths.dur.ac.uk/~dma0ds/

Volume 13, issue 2 (2013)