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Braid groups of non-orientable surfaces and the Fadell–Neuwirth short exact sequence by Daciberg Lima Gonçalves; John Guaschi is a Mathematics article available to read on EtoBox.

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Let M be a compact, connected non-orientable surface without boundary and of genus g 3. We investigate the pure braid groups P n (M) of M, and in particular the possible splitting of the Fadell-Neuwirth short exact sequence where m, n 1, and p \* is the homomorphism which corresponds geometrically to forgetting the last m strings. This problem is equivalent to that of the existence of a section for the associated fibration p: F n+m (M) -→ F n (M) of configuration spaces, defined by p((x 1 , . . . , x n , x n+1 , . . . , x n+m )) = (x 1 , . . . , x n ). We show that p and p \* admit a section if and only if n = 1. Together with previous results, this completes the resolution of the splitting problem for surface pure braid groups.

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Author

Daciberg Lima Gonçalves; John Guaschi

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0022-4049)

Published

2010

Language

EN

Field

Mathematics (Physical Sciences)