# Touching the $$Z_2$$ in Three-Dimensional Rotations

by Vesna Stojanoska and Orlin Stoytchev

Award: Carl B. Allendoerfer

Year of Award: 2009

Publication Information:Mathematics Magazine, vol. 81, no. 5, December 2008, pp. 345-357

Summary: If we compose two nontrivial complete rotations, the resulting motion can always be deformed to the null motion. This paper gives a mathematical formulation of this non-obvious geometric property.

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About the Authors

Vesna Stojanoska received her B.A. from the American University in Bulgaria and is now a Ph.D. student at Northwestern University. Her research is in algebraic topology: she is interested in using algebraic geometry and number theory to better understand various phenomena in stable homotopy theory.

Orlin Stoytchev is a professor at the American University in Bulgaria. He received his Ph.D. from Virginia Tech. His research interests can be summarized as “the different aspects of symmetries in mathematics and physics” and have led to works on Von Neumann algebras, representations of infinite-dimensional Lie groups and algebras, and recently on braid groups.

Subject classification(s): Algebra and Number Theory | Abstract Algebra | Groups | Algebra | Linear Algebra | Linear Transformations | Geometry and Topology | Topology
Publication Date:
Monday, August 24, 2009