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Higher Dimensional Kleinian Groups

My advisor says, I should invest a portion of my time, to something disjoint from my research area (= local connectedness of the boundary of relatively hyperbolic groups). Higher dimensional Kleinian groups are not exactly disjoint from that. Nevertheless they are somewhat of a different flavor. Might I say, more concrete, that the spiraling labyrinth of abstraction that Bowditch, Levitt, Bestvina and Rips have led me to.

Great minds of antiquity often indulged in ‘real’ world while doing the wonderful abstract mathematics seemingly divorced from that reality. For example Gauss did field surveys, Archimedes made weapons, and Newton observed falling apples (there! I said it). In 21st century, the discrete isometries of higher dimensional hyperbolic spaces are like the apples of Newton for me. Sometimes I wonder at the divorce of realism from the canons of abstraction.

I would begin by scanning Kapovich’s survey (February 2020): https://arxiv.org/pdf/math/0701370.pdf

Then I would probably move on to another survey by Tukia.

Presently I have a couple of students in the research track of Cheenta. I plan to set up a reading and exploration drive with them. The key curiosity is the limit set of higher dimensional Kleinian groups.

By Ashani Dasgupta

Pursuing Ph.D. in Geometric Group Theory at University of Wisconsin, Milwaukee

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