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The Euler characteristic of the configuration space of planar spidery linkages

Yasuhiko Kamiyama and Shuichi Tsukuda
Algebraic & Geometric Topology 14 (2014) 3659–3688
DOI: 10.2140/agt.2014.14.3659
Abstract

Among planar mechanical linkages, polygonal and spidery linkages are particularly important. We define a planar linkage which contains them. Constructing a Bott–Morse function on the configuration space of this, we determine the Euler characteristic. In particular, we give a new calculation of the Euler characteristic of polygon spaces.

Keywords
configuration space, planar linkage, Bott–Morse function
Mathematical Subject Classification 2010
Primary: 58E05
Secondary: 57M20
References
Publication
Received: 24 January 2014
Revised: 8 June 2014
Accepted: 10 June 2014
Published: 15 January 2015
Authors
Yasuhiko Kamiyama
Department of Mathematics
University of the Ryukyus
Nishihara-Cho, Okinawa 903-0213
Japan
Shuichi Tsukuda
Department of Mathematics
University of the Ryukyus
Nishihara-Cho, Okinawa 903-0213
Japan