Topology
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PERSONAL RESEARCH
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Published articles
D. H. Delphenich, “On the axioms of topological electromagnetism,” Ann. Phys. 14 (2005), 347-377.
D. H. Delphenich, “The homology of defective crystal lattices and the continuum limit,” Ann. Phys. (Berlin) 522 (2010), 874-903
arXiv.org uploads
D. H. Delphenich, “Foliated Cobordism and Motion,” arXiv:gr-qc/0209091
D. H. Delphenich, “Proper Time Foliations of Lorentz Manifolds,” arXiv:gr-qc/0211066
D. H. Delphenich, “Spacetime G-structures I: Topological Defects,” arXiv:gr-qc/0304016
D. H. Delphenich, “Spacetime G-structures II: geometry of the ground states,” arXiv:gr-qc/0401089
D. H. Delphenich, “Field/source duality in topological field theories,” arXiv:hep-th/0702105
D. H. Delphenich, “On the topological nature of Volterra's theorem,” arXiv:1109.2012
D. H. Delphenich, "The role of homology in fluid vortices I: non-relativistic flow," arXiv:1412.3059
D. H. Delphenich, "Homology, equilibrium, and conservation laws I: Discrete systems of points," arXiv:1901.03171
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TRANSLATIONS
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A. F. Möbius, “On the composition of line segments and a new way of founding the barycentric calculus that arises from it,” J. f. reine und angew. Math. 28 (1844), 1-9.
G. Kirchhoff, "On the solution of the equations to which one will be led in the study of linear distributions distributions of galvanic currents," Ann. Phys. Chem. 72 (1847), 497-508.
C. F. Gauss, "On electrodynamics," from Carl Friedrich Gauss Werke, vol. V, Kon. Ges. Wiss. Gottingen, 1867, pp. 605.
E. Schering, "Remarks on Gauss," from Carl Friedrich Gauss Werke, vol. V, Kon. Ges. Wiss. Gottingen, 1867, pp. 637-640.
L. Kronecker, "On systems of functions of several variables," Monatsber. Kon. preuss. Akad. Wiss. (1869), 159-193.
L. Kronecker, "On systems of functions of several variables," Monatsber. Kon. Akad. Wiss. (1869), 688-698.
E. Betti, "On spaces with an arbitrary number of dimensions," Ann. mat. pura appl. (2) 4 (1870-71), 140-158.
L. Kronecker, "On the characteristic of a system of functions," Monatsber. Kon. preuss. Akad. Wiss. (1878), 145-152.
W. Dyck, "Contributions to analysis situs. I," Math. Ann. 33 (1888), 457-463.
J. Hadamard, "Some applications of the Kronecker index," Note in J. Tannery, Introduction a la theory des fonctions d'une variable, v. II, Hermann, Paris, 1910, pp. 437-477.
L. E. J. Brouwer, "Proof of Jordan's theorem in n-dimensional space," Math. Ann. 71 (1912), 314-319.
H. Hopf, “On the curvatura integra of closed hypersurfaces,” Math. Ann. 95 (1927), 340-367.
L. Pontrjagin, "On the algebraic content of topological duality theorems," Math. Ann. 105 (1931), 165-205.
E. Stiefel, "Direction fields and teleparallelism in n-dimensional manifolds," Comm. Math. Helv. 25 (1935), 305-353.
H. Hopf, “Vector fields in n-dimensional manifolds,” Math. Ann. 96 (1936/37), 225-250.
G. Reeb, "On certain topological properties of trajectories of dynamical systems," Mem. Acad. Roy. Belg. tome 27, fasc. 9, 1952, Brussels.
A. Weil, "On de Rham's theorems," Comm. Math. Helv. 26 (1952), 119-145.
R. Thom, “Cobordant differentiable manifolds,” Coll. Intl. du C. N. R. S., v. LII, Géométrie différentielle, Strasbourg (1953), pp. 143-149.
R. Thom, "The classification of immersions," Seminaire Bourbaki (1956-58), exp. 157, pp. 279-289.
R. Thom, “The singularities of differentiable maps,” Ann. Inst. Fourier, Grenoble 6 (1) (1956), 43-87.
R. Thom, “Generalization of Morse theory to foliated manifolds,” Ann. Inst. Fourier, Grenoble 14 (1) (1964), 173-190.
J. Martinet, “On the singularities of differential forms,” Ann. Inst. Fourier, Grenoble 20 (1) (1970), 95-178.
R. Langevin, “Foliations, energies, and liquid crystals,” Soc. Math. France, Asterisque 107-108 (1983), 201-213.
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PERSONAL RESEARCH
______________________________________________________________________________________________________________________________________________________
Published articles
D. H. Delphenich, “On the axioms of topological electromagnetism,” Ann. Phys. 14 (2005), 347-377.
D. H. Delphenich, “The homology of defective crystal lattices and the continuum limit,” Ann. Phys. (Berlin) 522 (2010), 874-903
arXiv.org uploads
D. H. Delphenich, “Foliated Cobordism and Motion,” arXiv:gr-qc/0209091
D. H. Delphenich, “Proper Time Foliations of Lorentz Manifolds,” arXiv:gr-qc/0211066
D. H. Delphenich, “Spacetime G-structures I: Topological Defects,” arXiv:gr-qc/0304016
D. H. Delphenich, “Spacetime G-structures II: geometry of the ground states,” arXiv:gr-qc/0401089
D. H. Delphenich, “Field/source duality in topological field theories,” arXiv:hep-th/0702105
D. H. Delphenich, “On the topological nature of Volterra's theorem,” arXiv:1109.2012
D. H. Delphenich, "The role of homology in fluid vortices I: non-relativistic flow," arXiv:1412.3059
D. H. Delphenich, "Homology, equilibrium, and conservation laws I: Discrete systems of points," arXiv:1901.03171
_______________________________________________________________________________________________________________________________________________________
TRANSLATIONS
_______________________________________________________________________________________________________________________________________________________
A. F. Möbius, “On the composition of line segments and a new way of founding the barycentric calculus that arises from it,” J. f. reine und angew. Math. 28 (1844), 1-9.
G. Kirchhoff, "On the solution of the equations to which one will be led in the study of linear distributions distributions of galvanic currents," Ann. Phys. Chem. 72 (1847), 497-508.
C. F. Gauss, "On electrodynamics," from Carl Friedrich Gauss Werke, vol. V, Kon. Ges. Wiss. Gottingen, 1867, pp. 605.
E. Schering, "Remarks on Gauss," from Carl Friedrich Gauss Werke, vol. V, Kon. Ges. Wiss. Gottingen, 1867, pp. 637-640.
L. Kronecker, "On systems of functions of several variables," Monatsber. Kon. preuss. Akad. Wiss. (1869), 159-193.
L. Kronecker, "On systems of functions of several variables," Monatsber. Kon. Akad. Wiss. (1869), 688-698.
E. Betti, "On spaces with an arbitrary number of dimensions," Ann. mat. pura appl. (2) 4 (1870-71), 140-158.
L. Kronecker, "On the characteristic of a system of functions," Monatsber. Kon. preuss. Akad. Wiss. (1878), 145-152.
W. Dyck, "Contributions to analysis situs. I," Math. Ann. 33 (1888), 457-463.
J. Hadamard, "Some applications of the Kronecker index," Note in J. Tannery, Introduction a la theory des fonctions d'une variable, v. II, Hermann, Paris, 1910, pp. 437-477.
L. E. J. Brouwer, "Proof of Jordan's theorem in n-dimensional space," Math. Ann. 71 (1912), 314-319.
H. Hopf, “On the curvatura integra of closed hypersurfaces,” Math. Ann. 95 (1927), 340-367.
L. Pontrjagin, "On the algebraic content of topological duality theorems," Math. Ann. 105 (1931), 165-205.
E. Stiefel, "Direction fields and teleparallelism in n-dimensional manifolds," Comm. Math. Helv. 25 (1935), 305-353.
H. Hopf, “Vector fields in n-dimensional manifolds,” Math. Ann. 96 (1936/37), 225-250.
G. Reeb, "On certain topological properties of trajectories of dynamical systems," Mem. Acad. Roy. Belg. tome 27, fasc. 9, 1952, Brussels.
A. Weil, "On de Rham's theorems," Comm. Math. Helv. 26 (1952), 119-145.
R. Thom, “Cobordant differentiable manifolds,” Coll. Intl. du C. N. R. S., v. LII, Géométrie différentielle, Strasbourg (1953), pp. 143-149.
R. Thom, "The classification of immersions," Seminaire Bourbaki (1956-58), exp. 157, pp. 279-289.
R. Thom, “The singularities of differentiable maps,” Ann. Inst. Fourier, Grenoble 6 (1) (1956), 43-87.
R. Thom, “Generalization of Morse theory to foliated manifolds,” Ann. Inst. Fourier, Grenoble 14 (1) (1964), 173-190.
J. Martinet, “On the singularities of differential forms,” Ann. Inst. Fourier, Grenoble 20 (1) (1970), 95-178.
R. Langevin, “Foliations, energies, and liquid crystals,” Soc. Math. France, Asterisque 107-108 (1983), 201-213.
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