THE μ INVARIANT AND THE CASSON INVARIANT OF 3-MANIFOLDS OBTAINED BY SURGERY ON CLOSED PURE 3-BRAIDS

摘要

Let P_3 be the group of pure 3-braids and B = {(β-circumflex) is contained in S~3|β ∈ P~3} the set of closed pure 3-braids. We calculate the μ-invariant of the Z_2-homology spheres obtained by integral Dehn surgery on elements of B, and the Casson invariant of the Z-homology spheres obtained by surgery on algebraically split, closed pure n-braids.