- Title Information
- Title
- C^2-Morse functions on the Deligne-Mumford compactification of the moduli space
- Type of Resource (primo)
- dissertations
- Name:
Personal
- Name Part
- Chen, Changjie
- Role
- Role Term:
Text
- creator
- Name:
Personal
- Name Part
- Kahn, Jeremy
- Role
- Role Term:
Text
- Advisor
- Name:
Personal
- Name Part
- Breiner, Christine
- Role
- Role Term:
Text
- Reader
- Name:
Personal
- Name Part
- Schwartz, Richard
- Role
- Role Term:
Text
- Reader
- Name:
Corporate
- Name Part
- Brown University. Department of Mathematics
- Role
- Role Term:
Text
- sponsor
- Origin Information
- Copyright Date
- 2024
- Physical Description
- Extent
- , None p.
- digitalOrigin
- born digital
- Note:
thesis
- Thesis (Ph. D.)--Brown University, 2024
- Genre (aat)
- theses
- 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.
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/00940919")
- Topic
- Geometry, Differential
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/01145803")
- Topic
- Teichmüller spaces
- Subject
- Topic
- moduli space of curves
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/00940922")
- Topic
- Geometry, Hyperbolic
- Language
- Language Term (ISO639-2B)
- English
- Record Information
- Record Content Source (marcorg)
- RPB
- Record Creation Date
(encoding="iso8601")
- 20240501