C^2-Morse functions on the Deligne-Mumford compactification of the moduli space

Chen, Changjie

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Year:: 2024
Contributor:: Chen, Changjie (creator); Kahn, Jeremy (Advisor); Breiner, Christine (Reader); Schwartz, Richard (Reader); Brown University. Department of Mathematics (sponsor)
Genre:: theses
Subject:: Geometry, Differential; Teichmüller spaces; moduli space of curves; Geometry, Hyperbolic
Extent:: , None p.

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Abstract:: We present a series of C^2-Morse functions on the Deligne-Mumford compactification M_{g,n} bar of the moduli space of genus g Riemann/hyperbolic surfaces with n punctures. This series of functions converges to the systole function, which is topologically Morse. We will show that the critical points of our functions approach those of systole sublinearly, stratum-wise, and with the same indices. Our functions might be the first explicit examples of C^2-Morse functions on M_{g,n} bar, and the Morse handle decomposition may give rise to the first example of a natural cell decomposition of M_{g,n} bar, that works no matter if n is positive or equal to 0.
Notes:: Thesis (Ph. D.)--Brown University, 2024

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Citation

Chen, Changjie, "C^2-Morse functions on the Deligne-Mumford compactification of the moduli space" (2024). Mathematics Theses and Dissertations. Brown Digital Repository. Brown University Library. https://repository.library.brown.edu/studio/item/bdr:tbb6wgqu/

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Mathematics Theses and Dissertations

Theses and Dissertations for the Mathematics department.
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