Let Î£âˆž,1 be the inductive limit of compact oriented surfaces with one boundary component. We prove the center of the Goldman Lie algebra of the surface Î£âˆž,1 is spanned by the constant loop. A similarâ€¦ (More)

For each d â‰¥ 2, the mapping class group for plane curves of degree d will be defined and it is proved that there exists uniquely the Meyer function on this group. In the case of d = 4, using ourâ€¦ (More)

We present a formula expressing Earleâ€™s twisted 1-cocycle on the mapping class group of a closed oriented surface of genus â‰¥ 2 relative to a fixed base point, with coefficients in the first homologyâ€¦ (More)

We provide some language for algebraic study of the mapping class groups for surfaces with non-connected boundary. As applications, we generalize our previous results on Dehn twists in [13] and [17]â€¦ (More)

We present a formula expressing Earleâ€™s twisted 1-cocycle on the mapping class group of a closed oriented surface of genus â‰¥ 2 relative to a fixed base point, with coefficients in the first homologyâ€¦ (More)

A complete description of the global monodromy of a Lefschetz fibration arising from the Fermat surface of degree 4 is given. As a by-product we get a positive relation among right hand Dehn twistsâ€¦ (More)

By introducing an invariant of loops on a compact oriented surface with one boundary component, we give an explicit formula for the action of Dehn twists on the completed group ring of theâ€¦ (More)

We give a survey on Meyer functions, with emphasis on their application to the signatures of fibered 4-manifolds. 2000 Mathematics Subject Classification: 14D05, 20F34, 32G15; 57N13.