# Arunima Ray

Degrees

Rice University, Ph.D.State University of New York Geneseo, B.A.

Expertise

Geometric topology, particularly knot theory and its applications to 3- and 4-manifoldsProfile

The set of knots and links in 3-dimensional space is a group under a certain 4-dimensional equivalence relation called concordance. Broadly speaking, my research so far has sought to understand the structure of this group. The study of knots and links under this equivalence relation is related to the study of 4-manifolds; the fourth dimension is particularly difficult to study, since it is in some sense a boundary case between low and high dimensions - there are enough dimensions for the manifold topology to exhibit complex behavior, but not enough space for our usual tools to work. WebpageCourses Taught

MATH | 15a | Applied Linear Algebra |

MATH | 23b | Introduction to Proofs |

MATH | 100b | Introduction to Algebra, Part II |

MATH | 104a | Introduction to Topology |

MATH | 151a | Topology I |

MATH | 151b | Topology II |

Scholarship

Feller, Peter, Park, Junghwan, and Ray, Arunima. "The Upsilon invariant and satellite knots." (2016). (forthcoming)

Cochran, Tim D., Ray, Arunima. "Shake slice and shake concordant knots." (2015). (forthcoming)

Davis, Christopher W, Ray, Arunima. "Satellite operators as group actions on knot concordance." __Algebraic and Geometric Topology__ (2015). (forthcoming)

Davis, Christopher W., Ray, Arunima. "A new family links smoothly, but not topologically, concordant to the Hopf link." (2015). (forthcoming)

Ray, Arunima. "Casson towers and filtrations of the knot concordance group." __Algebraic and Geometric Topology__ 15. 2 (2015): 1119-1159.

Ray, Arunima. "Satellite operators with distinct iterates in smooth concordance." __Proceedings of the American Mathematical Society__ 143. 11 (2015): 5005-5020.

Cochran, Tim D., Davis, Christopher W., Ray, Arunima. "Injectivity of satellite operators in knot concordance." __Journal of Topology__ 7. 4 (2014): 948-964.

Ray, Arunima. __Casson towers and filtrations of the smooth knot concordance group__. Diss. Rice University, 4/16/2014. Proquest, 2014.

Ray, Arunima. "Slice knots which bound punctured Klein bottles." __Algebraic and Geometric Topology__ 13. 5 (2013): 2713-2731.