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Title:聽An infinite rank summand of the homology cobordism group

Abstract:聽We define an infinite family of integer-valued homology cobordism homomorphisms and prove that the homology cobordism group contains an infinite rank summand. The homomorphisms are defined using an algebraic modification of the involutive Heegaard Floer package of Hendricks-Manolescu and Hendricks-Manolescu-Zemke. This is joint work with Irving Dai, Jen Hom, and Matt Stroffregen.