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The Symplecticity of the Magnus Representation for Homology Cobordisms of Surfaces

Published online by Cambridge University Press:  17 April 2009

Takuya Sakasai
Takuya Sakasai
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, 3–8–1 Komaba, Meguro-ku, Tokyo 153–8914, Japan, e-mail: sakasai@ms.u-tokyo.ac.jp
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The Magnus matrix is an algebraic invariant assigned to each homology cobordism of a surface. We show that this matrix satisfies an equality which can be regarded as a non-commutative symplectic relation.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 76 , Issue 3 , December 2007 , pp. 421 - 431
Copyright
Copyright © Australian Mathematical Society 2007

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