We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Cut vertices in commutative graphs.
- Authors
CONANT, JAMES; GERLITS, FERENC; VOGTMANN, KAREN
- Abstract
The homology of Kontsevich's commutative graph complex parametrizes finite type invariants of odd-dimensional manifolds. This graph homology is also the twisted homology of Outer Space modulo its boundary, so gives a nice point of contact between geometric group theory and quantum topology. In this paper we give two different proofs (one algebraic, one geometric) that the commutative graph complex is quasi-isomorphic to the quotient complex obtained by modding out by graphs with cut vertices. This quotient complex has the advantage of being smaller and hence more practical for computations. In addition, it supports a Lie bialgebra structure coming from a bracket and cobracket we defined in a previous paper. As an application, we compute the rational homology groups of the commutative graph complex up to rank 7.
- Subjects
HOMOLOGY theory; HOMOLOGICAL algebra; COMMUTATIVE algebra; GRAPHIC methods; INVARIANTS (Mathematics); INFINITE-dimensional manifolds
- Publication
Quarterly Journal of Mathematics, 2005, Vol 56, Issue 3, p321
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmath/hah040