The Height of a Class in the Cohomology Ring of Polygon Spaces | Zendy

Yasuhiko Kamiyama | Zendy; Kazufumi Kimoto | Zendy

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The Height of a Class in the Cohomology Ring of Polygon Spaces

Author(s) -

Yasuhiko Kamiyama,

Kazufumi Kimoto

Publication year - 2013

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2013/305926

Subject(s) - mathematics , cohomology , modulo , isometry (riemannian geometry) , pure mathematics , cohomology ring , class (philosophy) , polygon (computer graphics) , ideal (ethics) , equivariant cohomology , ring (chemistry) , cover (algebra) , combinatorics , discrete mathematics , algebra over a field , computer science , engineering , mechanical engineering , telecommunications , philosophy , chemistry , organic chemistry , epistemology , frame (networking) , artificial intelligence

Let M-n,r be the configuration space of planar n-gons having side lengths 1,…,1 and r modulo isometry group. For generic r, the cohomology ring H*(M-n,r;ℤ2) has a form H*(M-n,r;ℤ2)=ℤ2[R(n,r),V1,…,Vn-1]/ℐn,r, where R(n,r) is the first Stiefel-Whitney class of a certain regular 2-cover π:Mn,r⟶M-n,r and the ideal ℐn,r is in general big. For generic r, we determine the number h(n,r) such that R(n,r)h(n,r)≠0 but R(n,r)h(n,r)+1=0

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