The Euler characteristic of the configuration space of planar spidery linkages

Kamiyama, Yasuhiko; Tsukuda, Shuichi

doi:10.2140/agt.2014.14.3659

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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

Volume 14, issue 6 (2014)