TY - JOUR
T1 - The Walker conjecture for chains in Rd
AU - Farber, Michael
AU - Hausmann, Jean Claude
AU - Schütz, Dirk
PY - 2011/9
Y1 - 2011/9
N2 - A chain is a configuration in l1.....n of segments of length 1.....n-1 consecutively joined to each other such that the resulting broken line connects two given points at a distance 1n. For a fixed generic set of length parameters the space of all chains in Rd is a closed smooth manifold of dimension (n-2)(d-1)-1. In this paper we study cohomology algebras of spaces of chains. We give a complete classification of these spaces (up to equivariant diffeomorphism) in terms of linear inequalities of a special kind which are satisfied by the length parameters l1.....n. This result is analogous to the conjecture of K. Walker which concerns the special case d=2. ©
AB - A chain is a configuration in l1.....n of segments of length 1.....n-1 consecutively joined to each other such that the resulting broken line connects two given points at a distance 1n. For a fixed generic set of length parameters the space of all chains in Rd is a closed smooth manifold of dimension (n-2)(d-1)-1. In this paper we study cohomology algebras of spaces of chains. We give a complete classification of these spaces (up to equivariant diffeomorphism) in terms of linear inequalities of a special kind which are satisfied by the length parameters l1.....n. This result is analogous to the conjecture of K. Walker which concerns the special case d=2. ©
UR - https://www.scopus.com/pages/publications/80054910892
U2 - 10.1017/S030500411100020X
DO - 10.1017/S030500411100020X
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:80054910892
SN - 0305-0041
VL - 151
SP - 283
EP - 292
JO - Mathematical Proceedings of the Cambridge Philosophical Society
JF - Mathematical Proceedings of the Cambridge Philosophical Society
IS - 2
ER -