Alexandria Digital Research Library

The Structure of Fundamental Groups of Smooth Metric Measure Spaces

Author:
Jaramillo, Maree Trisha Afaga
Degree Grantor:
University of California, Santa Barbara. Mathematics
Degree Supervisor:
Guofang Wei
Place of Publication:
[Santa Barbara, Calif.]
Publisher:
University of California, Santa Barbara
Creation Date:
2014
Issued Date:
2014
Topics:
Mathematics
Keywords:
Smooth Metric Measure Spaces
Bakry-Emery Ricci Curvature
Fundamental Groups
Differential Geometry
Genres:
Dissertations, Academic and Online resources
Dissertation:
Ph.D.--University of California, Santa Barbara, 2014
Description:

In this dissertation, we investigate the structure of fundamental groups of smooth metric measure spaces with Bakry-Emery Ricci tensor bounded from below. In particular, we generalize a result of Gabjin Yun to show that if a smooth metric measure space has almost nonnegative Bakry-Emery Ricci tensor and a lower bound on volume, then its fundamental group is almost abelian. We also generalize a result of Vitali Kapovitch and Burkhard Wilking to show that there is a uniform bound on the number of generators of the fundamental groups of smooth metric measure spaces with Bakry-Emery Ricci tensor bounded from below. In order to utilize the proof techniques of Yun and Kapovitch-Wilking, we extend many valuable tools for studying Riemannian manifolds with Ricci curvature bounded from below to the smooth metric measure space setting. In particular, we extend Jeff Cheeger and Tobias Colding's Splitting Theorem, which plays a key role in the proofs of our results on fundamental groups.

Physical Description:
1 online resource (97 pages)
Format:
Text
Collection(s):
UCSB electronic theses and dissertations
ARK:
ark:/48907/f3668b9x
ISBN:
9781321202045
Catalog System Number:
990045115900203776
Rights:
Inc.icon only.dark In Copyright
Copyright Holder:
Maree Jaramillo
File Description
Access: Public access
Jaramillo_ucsb_0035D_12162.pdf pdf (Portable Document Format)