李 昇 郁

Geometry, Topology and Physics, Mikio Nakahara, 2nd Edition, Graduate Student Series in Physics, Taylor & Francis, 2003. The 1st Edition of the book is available online through the University Libraries.

Homology Groups, Homotopy Groups, Differentiable Manifolds, de Rham Cohomology Groups, Riemannian Geometry, Complex Manifolds, Fibre Bundles, Characteristic Classes, Index Theorems

Monday/Wednesday 5:00-6:15pm in SH 304

Monday/Wednesday 3:30-5:00pm and by appointment

There are no exams. The average of grades you earned from homework assignments will be the main part of your final grade for the course.

Lecture notes are available as blog entries. Click on the links to view the notes.

• Lecture Notes 1: Matrix Lie Groups
• Lecture Notes 2: The Lie Algebra of the Orthogonal Group \(\mathrm{O}(n)\) (\(\mathrm{SO}(n)\))
• Lecture Notes 3: Orthogonal Group \(\mathrm{O}(n)\) and Symmetry
• Lecture Notes 4: Lorentz Group
• Lecture Notes 5: Lie Brackets (for \(n\times n\) Matrices)
• Lecture Notes 6: More Examples of Lie Groups: 3-Sphere as a Lie Group, The 3-Dimensional Heisenberg Group
• Lecture Notes 7: Lie Group Actions and Lie Group Representations
• Lecture Notes 8: Irreducible Representations of \(\mathrm{U}(1)\)
• Lecture Notes 9: The Representations of \(\mathrm{SU}(2)\)
• Lecture Notes 10: Fibre Bundles
• Lecture Notes 11: Differentiable Manifolds and Tangent Spaces
• Lecture Notes 12: Vector Bundles
• Lecture Notes 13: Line Bundles
• Lecture Notes 14: Sections of a Line Bundle I
• Lecture Notes 15: Sections of a Line Bundle II: Gauge Potential, Gauge Transformation, and Field Strength
• Lecture Notes 16: Parallel Transport, Holonomy, and Curvature

• Mathematics

• A Basic Course in Algebraic Topology, Graduate Texts in Mathematics, v. 127, William S. Massey, Springer, 1997. Cook Library has a copy. The call number is QA612 .M374 1991b.
• Algebraic Topology: An Introduction, Graduate Texts in Mathematics, v. 56, William S. Massey, Springer, 1990. Cook Library has a copy. The call number is QA611 .M343.
• Algebraic Topology Book by Allen Hatcher. Free to download.
  
• An Elementary Introduction to Groups and Representations, Brian C. Hall
  
• An Introduction to Differentiable Manifolds and Riemannian Geometry, Pure and Applied Mathematics, v. 120, 2nd Edition, William M. Boothby, Academic Press, 2002. Cook Library has a copy. The call number is QA3 .P8 vol.63. A copy of 2nd edition is available at Gulf Coast Library. In order to get this copy, you need to request it through the library's Document Delivery Service. It is free of charge.
• Basic Concepts of Algebraic Topology, Undergraduate Texts in Mathematics, Fred H. Croom, Springer, 1978. Cook Library has a copy. The call number is QA612 .C75.
• Basic Topology, Undergraduate Texts in Mathematics, Mark A. Armstrong, Springer, 1997.
  
• Elementary Differential Geometry, Barrett O'Neill, 2nd Edition, Academic Press, 2006. Cook Library has a copy of 1st edition and a copy of 2nd edition. Their call numbers are QA641 .O5 and QA641 .O5 1997, respectively. A copy of 2nd edition is also available at Gulf Coast Library. In order to get this copy, you need to request it through the library's Document Delivery Service. It is free of charge.
• Elementary Differential Geometry, Springer Undergraduate Mathematics Series, Andrew Pressley, Springer, 2002. Cook Library has a copy. The call number is QA641 .P68 2001. A copy is also available at Gulf Coast Library. In order to get this copy, you need to request it through  the library's Document Delivery Service. It is free of charge.
• Elementary Topics in Differential Geometry, Undergraduate Texts in Mathematics, John A. Thorpe, Springer, 1994. Cook Library has a copy. The call number is QA641 .T36.
  
• Elements of Algebraic Topology, James R. Munkres, Westview Press, 1995. Cook Library has a copy. The call number is QA612 .M86 1984b.
• Lecture Notes on Elementary Topology and Geometry, Undergraduate Texts in Mathematics, Isidore M. Singer and John A. Thorpe, Springer, 1976. Gulf Coast Library has a copy. The call number is QA611 .S498 1976. In order to get this copy, you need to request it through the library's Document Delivery Service. It is free of charge.
• Lie Groups, Lie Algebras, and Representations: An Elementary Introduction, Graduate Texts in Mathematics, v. 222, Corr. 2nd Printing, Brian C. Hall, Springer, 2004. This book is the published version of Brian C. Hall's lecture notes listed in #4, which is freely available on the arxiv.org. Cook Library has a copy. The call number is QA387 .H34 2003.
• Notes on Seiberg-Witten Gauge Theory, Matilde Marcolli
  
• Riemannian Geometry, Manfredo Perdigão do Carmo, Birkhäuser, 1992. Gulf Coast Library has a copy. The call number is QA649 .C2913 1992. In order to get this copy, you need to request it through the library's Document Delivery Service. It is free of charge.
• Topology, Geometry, and Gauge Fields: Foundations, Texts in Applied Mathematics, v. 25, Gregory L. Naber, Springer, 1997. Cook Library has a copy. The call number is QC20.7.T65 N33 1997. A copy is also available at Gulf Coast Library. In order to get this copy, you need to request it through  the library's Document Delivery Service. It is free of charge.
• Seiberg-Witten Gauge Theory, Texts and Readings in Mathematics, v. 17, Matilde Marcolli, Hindustan Book Agency, 1999. This book is the published version of Matilde Marcolli's lecture notes listed above, which is freely available on the arxiv.org. Cook Library has a copy. The call number is QA613.2 .M374 1999. A copy is also available at Gulf Coast Library. In order to get this copy, you need to request it through the library's Document Delivery Service. It is free of charge.
  
• Semi-Simple Lie Algebras and Their Representations, Robert N. Cahn, Benjamin-Cummings, 1984. Free to Download.
• Topology, James R. Munkres, 2nd Edition, Prentice-Hall, 2000. Gulf Coast Library has a copy. The call number is QA611 .M82. In order to get this copy, you need to request it through the library's Document Delivery Service. It is free of charge.

• Physics

• Aspects of Chern-Simons Theory, Gerald V. Dunne
• BUSSTEPP Lectures on String Theory, Richard J. Szabo
• D-Brane Primer, Clifford V. Johnson
• D-Branes, Cambridge Monographs on Mathematical Physics, Clifford V. Johnson, Cambridge University Press, 2006. This book is much extended and the published version of Clifford Johnson's lecture notes listed above. A copy is available online through the University Libraries.
• Introduction to String Theory, Thomas Mohaupt
• Introduction to Superstring Theory, E. Kiritsis
• Monopoles, Instantons and Confinement, Gerard 't Hooft, Falk Bruckmann
• Preparation for Gauge Theory, George Svetlichny
• Topology and physics-a historic essay, C. Nash