Atlas: Discrete cocompact subgroups of connected nilpotent groups and related flows by Paul Milnes

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SumTopo 2001, Sixteenth Summer Conference on Topology and its Applications
July 18-21, 2001
City College of CUNY
New York, NY, USA

Organizers
Ralph Kopperman (City College, CUNY), Susan Andima (CW Post College, LIU), Gerald Itzkowitz (Queens College, CUNY), Prabudh Misra (College of Staten Island, CUNY), Shelly Rothman (CW Post College, LIU), Aaron Todd (Baruch College, CUNY)

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Discrete cocompact subgroups of connected nilpotent groups and related flows
by
Paul Milnes
Univ. of Western Ontario

The 3-dimensional Heisenberg group G₃ ( = R³ as a set) has multiplication

(k, m, n)(k', m', n') = (k + k'+ nm', m + m', n + n')

and discrete cocompact (dc) subgroup H₃ = Z³ in G₃; the related flows are (Z, T) generated by the homeomorphism h: v --> av of the circle T for a = e^{2i\pi(\theta)} not a root of unity. The unitaries U(f)(v) = f(h(v)) and V(f)(v) = vf(v), for f in L²(T) and v in T, give a representation of H₃ generating the irrational rotation algebra A_\theta, a simple quotient of the group C^*-algebra of H₃. In this talk we will discuss the classification of the dc subgroups and related flows for G₃ and some higher dimensional connected nilpotent groups.

Date received: May 3, 2001