Subject Area
Mathematics
Description
Adam Banatwala ’22, Majors: Mathematics and Finance
Jensen Barry ’22, Majors: Biology and Mathematics
Mackenzie Maude ’22, Majors: Mathematics and Art History
Faculty Mentor: Dr. C. Joanna Su, Mathematics and Computer Science
One of the main topics in topology is the classification and comparison of shapes and surfaces. Since Spring 2020, our research group has been using symmetry groups to classify the 1- and 2-dimensional orientable and non-orientable closed surfaces.
First, the group worked on the symmetry groups of the 1- and 2-dimensional orientable closed surfaces; namely, the classification on V?? 1 (the one-point adjoint of n circles) and ?n (connected sum of n tori). Next, the group focused on classifications of 2-dimensional non-orientable closed surfaces, building upon previous results. The students established a relationship between the order of these symmetry groups on ?n (the connected sum of n Klein bottles) and ?n (the connected sum of n projective planes).
The group then proceeded to classify more complex 2-dimensional non-orientable closed surfaces. The focus was on those surfaces which were the connected sums of orientable and non-orientable surfaces. For these, the students discovered a formula for the order of the symmetry groups of Km#Tn and Pm#Tn respectively.
This completed the classification of 1- and 2-dimensional closed surfaces through the use of symmetry groups. This same methodology could further apply to closed manifolds of higher dimensions as well.
Publisher
Providence College
Date
4-27-2022
Type
Poster
Format
Text
Language
English
