Discussion Overview
The discussion revolves around two books on geometry: "Modern Geometry-Methods and Applications" by A.T. Fomenko and S.P. Novikov, and "Principles of Algebraic Geometry" by Phillip Griffiths and Joseph Harris. Participants explore the differences between these texts and their suitability for physicists, focusing on their content and applications in physics.
Discussion Character
- Debate/contested
- Technical explanation
Main Points Raised
- Some participants suggest that Fomenko and Novikov's book is more accessible and useful for physicists, covering geometry and topology of smooth manifolds from both differential and algebraic viewpoints.
- Others argue that Griffiths and Harris's book, while a standard reference in algebraic geometry, focuses on complex manifolds and may be less applicable to physics, particularly in areas like string theory.
- One participant notes that algebraic geometry can handle singularities that are not permitted in manifold theory, indicating a distinction in the types of mathematical objects each book addresses.
Areas of Agreement / Disagreement
Participants express differing opinions on the utility of each book for physicists, with no consensus on which is definitively more suitable.
Contextual Notes
There are unresolved questions regarding the specific applications of each book in physics and the extent to which their content overlaps or diverges in terms of usefulness for different areas of study.