Surgery exact triangles in involutive Heegaard Floer homology

Abstract: We establish a surgery exact triangle for involutive Heegaard Floer homology by using a doubling model of the involution. We use this exact triangle to give an involutive version of Ozsv\'ath-Szab\'o's mapping cone formula for knot surgery. As an application, we use this surgery formula to give examples of integer homology spheres that are not homology cobordant to any linear combination of Seifert fibered spaces.