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Thesis.pdf (582.64 KB)
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Barycentric Straightening, Splitting Rank and Bounded Cohomology
Author Info
Wang, Shi
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1466552761
Abstract Details
Year and Degree
2016, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
This work is devoted to the study of bounded cohomology from a geometric point of view. In the context of non-compact, connected, semisimple Lie groups with finite center, Dupont raised the question of whether the comparison map is always surjective. The main goal of this work is to show Dupont's conjecture in high degrees. We introduce the barycentric straightening and show that the straightened simplices in higher rank symmetric spaces of non-compact type has uniformly bounded volume, when the dimension of the simplices are close to the dimension of the symmetric spaces. We also give counterexamples where the barycentrically straightened simplices have unbounded volume when the dimension is equal to the splitting rank. This provides an obstruction to our straightening method. In addition, we compute explicitly this splitting rank for all symmetric spaces.
Committee
Jean Lafont (Advisor)
Michael Davis (Committee Member)
James Fowler (Committee Member)
Pages
82 p.
Subject Headings
Mathematics
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Citations
Wang, S. (2016).
Barycentric Straightening, Splitting Rank and Bounded Cohomology
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1466552761
APA Style (7th edition)
Wang, Shi.
Barycentric Straightening, Splitting Rank and Bounded Cohomology.
2016. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1466552761.
MLA Style (8th edition)
Wang, Shi. "Barycentric Straightening, Splitting Rank and Bounded Cohomology." Doctoral dissertation, Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1466552761
Chicago Manual of Style (17th edition)
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Document number:
osu1466552761
Download Count:
375
Copyright Info
© 2016, some rights reserved.
Barycentric Straightening, Splitting Rank and Bounded Cohomology by Shi Wang is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by The Ohio State University and OhioLINK.