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: 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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DOI:
https://doi.org/10.1090/S0025-5718-1969-0246820-9

Article copyright:
© Copyright 1969
American Mathematical Society