Title: On the Secondary Upsilon Invariant Authors: Xu, Xiaoyu Advisors: Szabo, ZoltanOzsvath, Peter Department: Mathematics Class Year: 2018 Abstract: In this paper we construct an infinite family of knots with vanishing Upsilon invariant $\Upsilon$, although their secondary Upsilon invariants $\Upsilon^2$ show that they are linearly independent in the smooth knot concordance group. We also prove a conjecture in a paper by Allen. URI: http://arks.princeton.edu/ark:/88435/dsp019880vt721 Type of Material: Princeton University Senior Theses Language: en Appears in Collections: Mathematics, 1934-2020