Zariski dense surface subgroups in SL(4,Z)
نویسندگان
چکیده
The result of [6] is the existence of an infinite family of Zariski dense surface subgroups of fixed genus inside SL(3,Z); here we exhibit such subgroups inside SL(4,Z) and symplectic groups. In this setting the power of such a result comes in large part from the conclusion that the groups are Zariski dense the existence of surface groups inside SL(4,Z) can be proved fairly easily, since it’s not hard to see that there is a faithful representation of the figure eight knot group into SL(4,Z) (see the end of §4) and surface groups follow immediately. However this image lies in a six dimensional Lie subgroup of SL(4,R) and so in particular is not Zariski dense in SL(4,R). The main result of this paper is the following:
منابع مشابه
Zariski dense surface subgroups in SL(3,Z)
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