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Query regarding group theory and geometry

5 years ago in Discussion By Krishan Pancholi

Research Objectives

Although I have completed my Master’s in mathematics, I still have query regarding group theory and geometry.

All Answers (2 Answers In All)

By Sneha Answered 5 years ago

Consider a surface made of thin, easily stretchable rubber. Bend, stretch, and deform this surface. As you deform the surface, it will change in many ways, but some aspects of its nature will stay the same. The aspect of a surface’s nature which is unaffected by deformation is called the topology of the surface. A surface’s geometry consists of those properties which do change when the surface is deformed.

By Vineet Answered 5 years ago

Hello Krishan. In simple words, geometry deals with shapes, relative positions and size of figures, properties of space etc. Whereas topology studies the properties of space that are preserved under continuous deformation. For example, for a geometer a bowl and a sphere are not the same because the curvature and the metric changes. But for a topologist, both are the same. This is because one can deform into the other. Checkout https://www.youtube.com/watch?v=G4XRFZZNxtc. This video explains you about the topology and geometry of the surface. You can also check http://virtualmath1.stanford.edu/~ralph/math215b/Bredon.pdf, https://zodml.org/sites/default/files/Introduction_to_Topology_and_Geometry%2C_2_edition.pdf. Don’t just stick onto one website. There are several online lectures / tutorials that can educate you about both the topics.