Tohoku Mathematical Journal
2003
December
SECOND SERIES VOL. 55, NO. 4

Tohoku Math. J.
55 (2003), 543-549

Title SOME HOMOLOGICAL INVARIANTS OF THE MAPPING CLASS GROUP OF A THREE-DIMENSIONAL HANDLEBODY

Author Susumu Hirose

(Received December 5, 2001, revised September 17, 2002)
Abstract. We show that, if $g \geq 2$, the virtual cohomological dimension of the mapping class group of a three-dimensional handlebody of genus $g$ is equal to $4g-5$ and its Euler number is equal to 0.

2000 Mathematics Subject Classification. Primary 57N10; Secondary 57N05, 20F38.
Key words and phrases. Virtual cohomological dimension, Euler number, 3-dimensional handlebody, mapping class group.

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