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

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]**Harvey Cohn,*A numerical survey of the floors of various Hilbert fundamental domains*, Math. Comp.**19**(1965), 594–605. MR**0195818**, 10.1090/S0025-5718-1965-0195818-4**[12]**Harvey Cohn,*A numerical study of topological features of certain Hilbert fundamental domains*, Math. Comp.**21**(1967), 76–86. MR**0222029**, 10.1090/S0025-5718-1967-0222029-8**[13]**Harvey Cohn,*Sphere fibration induced by uniformization of modular group*, J. London Math. Soc.**43**(1968), 10–20. MR**0228435**

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

Article copyright:
© Copyright 1969
American Mathematical Society