@article{chang_manion_2023, title={COMPATIBILITY IN OZSVaTH-SZAB & Oacute; 'S BORDERED HFK VIA HIGHER REPRESENTATIONS}, volume={323}, ISSN={["1945-5844"]}, DOI={10.2140/pjm.2023.323.253}, abstractNote={We equip the basic local crossing bimodules in Ozsv\'ath-Szab\'o's theory of bordered knot Floer homology with the structure of 1-morphisms of 2-representations, categorifying the $U_q(\mathfrak{gl}(1|1)^+)$-intertwining property of the corresponding maps between ordinary representations. Besides yielding a new connection between bordered knot Floer homology and higher representation theory in line with work of Rouquier and the second author, this structure gives an algebraic reformulation of a ``compatibility between summands'' property for Ozsv\'ath-Szab\'o's bimodules that is important when building their theory up from local crossings to more global tangles and knots.}, number={2}, journal={PACIFIC JOURNAL OF MATHEMATICS}, author={Chang, William and Manion, Andrew}, year={2023}, month={Apr} }
 @article{gu_manion_2023, title={Evaluations of Link Polynomials and Recent Constructions in Heegaard Floer Theory}, volume={73}, ISSN={["1945-2365"]}, DOI={10.1307/mmj/20216061}, abstractNote={Using a definition of Euler characteristic for fractionally-graded complexes based on roots of unity, we show that the Euler characteristics of Dowlin's"$\mathfrak{sl}(n)$-like"Heegaard Floer knot invariants $HFK_n$ recover both Alexander polynomial evaluations and $\mathfrak{sl}(n)$ polynomial evaluations at certain roots of unity for links in $S^3$. We show that the equality of these evaluations can be viewed as the decategorified content of the conjectured spectral sequences relating $\mathfrak{sl}(n)$ homology and $HFK_n$.}, number={5}, journal={MICHIGAN MATHEMATICAL JOURNAL}, author={Gu, Larry and Manion, Andrew}, year={2023}, month={Nov}, pages={1097–1118} }
 @article{lauda_licata_manion_2023, title={Strands algebras and the affine highest weight property for equivariant hypertoric categories}, volume={413}, ISSN={["1090-2082"]}, DOI={10.1016/j.aim.2022.108849}, abstractNote={We show that the equivariant hypertoric convolution algebras introduced by Braden-Licata-Proudfoot-Webster are affine quasi hereditary in the sense of Kleshchev and compute the Ext groups between standard modules. Together with the main result of arXiv:2009.03981, this implies a number of new homological results about the bordered Floer algebras of Ozsvath-Szabo, including the existence of standard modules over these algebras. We prove that the Ext groups between standard modules are isomorphic to the homology of a variant of the Lipshitz-Ozsvath-Thurston bordered strands dg algebras.}, journal={ADVANCES IN MATHEMATICS}, author={Lauda, Aaron D. and Licata, Anthony M. and Manion, Andrew}, year={2023}, month={Jan} }
 @article{manion_2023, title={Surface Gluing with Signs and Gradings in Decategorified Heegaard Floer Theory}, ISSN={["1687-0247"]}, DOI={10.1093/imrn/rnad238}, abstractNote={Abstract}, journal={INTERNATIONAL MATHEMATICS RESEARCH NOTICES}, author={Manion, Andrew}, year={2023}, month={Oct} }