Some computer-assisted topological models of Hilbert fundamental domains
Author:
Harvey Cohn
Journal:
Math. Comp. 23 (1969), 475-487
MSC:
Primary 10.21; Secondary 68.00
DOI:
https://doi.org/10.1090/S0025-5718-1969-0246820-9
MathSciNet review:
0246820
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Abstract | References | Similar Articles | Additional Information
Abstract: The Hubert modular group for the integral domain
has a fourdimensional fundamental domain
which should be represented geometrically (like the classic modular group). Computer assistance (by the Argonne CDC 3600) was used for outlining cross sections of the three-dimensional "floor" of
, which is a mosaic of an intractably large number of boundary pieces identified under
. The cross sections shown here might well contain enough information when
to form some "incidence matrices" and see
(at least) combinatorially. For special symmetrized subgroups of
, it is plausible to see homologously independent
-spheres in (the corresponding)
. The program is a continuation of one outlined in two earlier issues of this journal v. 19, 1965, pp. 594-605, MR 33 #4016, and v. 21, 1967, pp. 76-86, MR 36 #5081.
- [6] H. Cohn, "A numerical survey of the floors of various Hilbert fundamental domains," Math. Comp., v. 19, 1965, pp. 594-605. MR 33 #4016. MR 0195818 (33:4016)
- [12] H. Cohn, "A numerical study of topological features of certain Hilbert fundamental domains," Math Comp., v. 21, 1967, pp. 76-86. MR 36 #5081. MR 0222029 (36:5081)
- [13]
H. Cohn, "Sphere fibration induced by uniformization of modular group," J. London Math. Soc., v. 43, 1968, pp. 10-20. Erratum in [6] p. 603, Table 3. For
,
(not 3). Errata in [12] p. 81, Figure 2. Instead of
, read
. p. 82, Figure 3. Instead of
, read
,
,
,
,
. pp. 84-85, Figure 4. Instead of
, read
. MR 0228435 (37:4015)
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Additional Information
DOI:
https://doi.org/10.1090/S0025-5718-1969-0246820-9
Article copyright:
© Copyright 1969
American Mathematical Society