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

Schuetz, Dirk

Abstract

We study the topology of moduli spaces of closed linkages in ℝd depending on a length vector ℓ ∈ ℝn. 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.

• Journal Article Type: Article
• Publication Date: Jan 1, 2013
• Deposit Date: Apr 24, 2013
• Publicly Available Date: May 2, 2013
• Journal: Algebraic and Geometric Topology
• Print ISSN: 1472-2747
• Electronic ISSN: 1472-2739
• Publisher: Mathematical Sciences Publishers (MSP)
• Peer Reviewed: Peer Reviewed
• Volume: 13
• Issue: 2
• Pages: 1183-1224
• DOI: https://doi.org/10.2140/agt.2013.13.1183
• Keywords: Moduli spaces, Linkages, Homology.
• Public URL: https://durham-repository.worktribe.com/output/1455777