1. Adkins, W. A. and S. H. Weintraub, Algebra: An Approach via Module Theory, 307-327, Springer-Verlag, New York, 1992.
2. Armstrong, M., Basic Topology, Springer-Verlag, New York, 1983.
doi:10.1007/978-1-4757-1793-8
3. Balabanian, N. and T. A. Bickart, Electrical Network Theory, 80, John Wiley and Sons, New York, 1969.
4. Bamberg, P. and S. Sternberg, A Course in Mathematics for Students of Physics: 2, Ch. 12, Cambridge U. Press, NY, 1990.
5. Bossavit, A., A. Vourdas, and K. J. Binns, "Magnetostatics with scalar potentials in multiply connected regions," IEE Proc. A, Vol. 136, 260-261, 1989.
6. Bott, R. and L. W. Tu, Differential Forms in Algebraic Topology, 40-42, 51, 234, 258, 240, Springer-Verlag, New York, 1982.
doi:10.1007/978-1-4757-3951-0
7. Brown, M. L., "Scalar potentials in multiply connected regions," Int. J. Numer. Meth. Eng., Vol. 20, 665-680, 1984.
doi:10.1002/nme.1620200406
8. Cohen, H., A Course in Computational Algebraic Number Theory, Springer-Verlag, New York, 1993.
doi:10.1007/978-3-662-02945-9
9. Coleman, T. F., A. Edenbrandt, and J. R. Gilbert, "Predicting fill for sparse orthogonal factorization," Journal of the Association for Computing Machinery, Vol. 33, 517-532, 1986.
doi:10.1145/5925.5932
10. Croom, F. H., Basic Concepts of Algebraic Topology, Chaps. 2, 7.3, 4.5, Springer-Verlag, New York, 1978.
doi:10.1007/978-1-4684-9475-4
11. Deschamps, G. A., "Electromagnetics and differential forms," IEEE Proc., Vol. 69, 676-696, 1981.
doi:10.1109/PROC.1981.12048
12. Greenberg, M. J. and J. R. Harper, Algebraic Topology, 235, 63–66 Benjamin/Cummings, Reading, MA, 1981.
13. Gross, P. W., "The commutator subgroup of the first homotopy group and cuts for scalar potentials in multiply connected regions,", Master’s thesis, Dept. of Biomed. Eng., Boston U., September 1993.
14. Gross, P. W. and P. R. Kotiuga, "Data structures for geometric and topological aspects of finite element algorithms,", this volume.
15. Gross, P. W. and P. R. Kotiuga, "A challenge for magnetic scalar potential formulations of 3-d eddy current problems: Multiply connected cuts in multiply connected regions which necessarily leave the cut complement multiply connected," Electric and Magnetic Fields: From Numerical Models to Industrial Applications, A. Nicolet and R. Belmans (eds.), Plenum, 1–20, New York, 1995. Proc. of the Second Int. Workshop on Electric and Magnetic Fields.
16. Guillemin, V. and A. Pollack, Differential Topology, 21, Prentice- Hall, Englewood Cliffs, New Jersey, 1974.
17. Gunning, R. C. and H. Rossi, Analytic Functions of Several Complex Variables, Prentice-Hall, Englewood Cliffs, N.J., 1965.
18. Harrold, C. S. and J. Simkin, "Cutting multiply connected domains," IEEE Trans. Magn., Vol. 21, 2495-2498, 1985.
doi:10.1109/TMAG.1985.1064142
19. Kotiuga, P. R., "Hodge decompositions and computational electromagnetics,", Ph.D. thesis, McGill University, Montreal, 1984.
20. Kotiuga, P. R., "On making cuts for magnetic scalar potentials in multiply connected regions," J. Appl. Phys., Vol. 61, 3916-3918, 1987.
doi:10.1063/1.338583
21. Kotiuga, P. R., "An algorithm to make cuts for scalar potentials in tetrahedral meshes based on the finite element method," IEEE Trans. Magn., Vol. 25, 4129-4131, 1989.
doi:10.1109/20.42544
22. Kotiuga, P. R., "Topological considerations in coupling scalar potentials to stream functions describing surface currents," IEEE Trans. Magn., Vol. 25, 2925-2927, 1989.
doi:10.1109/20.34326
23. Kotiuga, P. R., "Analysis of finite-element matrices arising from discretizations of helicity functionals," J. Appl. Phys., Vol. 67, 5815-5817, 1990.
doi:10.1063/1.345973
24. Kotiuga, P. R., "Topological duality in three-dimensional eddycurrent problems and its role in computer-aided problem formulation," J. Appl. Phys., Vol. 67, 4717-4719, 1990.
doi:10.1063/1.344812
25. Kotiuga, P. R., "Essential arithmetic for evaluating three dimensional vector finite element interpolation schemes," IEEE Trans. Magn., Vol. 27, 5208-5210, 1991.
doi:10.1109/20.278789
26. Kotiuga, P. R., A. Vourdas, and K. J. Binns, "Magnetostatics with scalar potentials in multiply connected regions," IEE Proc. A, Vol. 137, 231-232, 1990.
27. Maxwell, J. C., A Treatise on Electricity and Magnetism (1891), Chap. 1, Art. 18–22, Dover, New York, 1954.
28. Munkres, J. R., Elements of Algebraic Topology, 377-380, Addison-Wesley, Reading, MA, 1984.
29. Murphy, A., "Implementation of a finite element based algorithm to make cuts for magnetic scalar potentials,", Master’s thesis, Dept. of ECS Eng., Boston U., 1991.
30. Pothen, A. and C.-J. Fan, "Computing the block triangular form of a sparse matrix," ACM Transactions on Mathematical Software, Vol. 16, 303-324, 1990.
doi:10.1145/98267.98287
31. Ren, Z. and A. Razek, "Boundary edge elements and spanning tree technique in three-dimensional electromagnetic field computation," Int. J. Num. Meth. Eng., Vol. 36, 2877-2893, 1993.
doi:10.1002/nme.1620361703
32. Rotman, J. J., An Introduction to Algebraic Topology, Springer- Verlag, NY, 1988.
doi:10.1007/978-1-4612-4576-6
33. Saitoh, I., "Perturbed H-method without the Lagrange multiplier for three dimensional nonlinear magnetostatic problems," IEEE Trans. Magn., Vol. 30, 4302-4304, 1994.
doi:10.1109/20.334068
34. Silvester, P. and R. Ferrari, Finite Elements for Electrical Engineers, 2nd Edition, Cambridge U. Press, NY, 1990.
35. Stillwell, J., Classical Topology and Combinatorial Group Theory, Second Edition, Ch. 3,4, Springer-Verlag, NY, 1993.
doi:10.1007/978-1-4612-4372-4
36. Thurston, W. P., Three-Dimensional Geometry and Topology, Princeton University Press, Princeton, New Jersey, 1997.
doi:10.1515/9781400865321
37. Vourdas, A., K. J. Binns, and , "Magnetostatics with scalar potentials in multiply connected regions," IEE Proc. A, Vol. 136, 49-54, 1989.