4 papers
Real Heegaard Floer homology with integral coefficients
Ciprian Mircea Bonciocat
We treat the question of upgrading Guth-Manolescu's real Heegaard Floer theory to a -graded invariant defined over , specifically for the hat version with o…
Floer homotopy theory for monotone Lagrangians
Ciprian Mircea Bonciocat
We circumvent one of the roadblocks in associating Floer homotopy types to monotone Lagrangians, namely the curvature phenomena occurring in high dimensions. Given and $R…
Parameterized Lagrangian Floer homotopy
Kenneth Blakey, Ciprian Mircea Bonciocat
We construct the Lagrangian Floer homotopy type, in the exact setting, as a spectrum parameterized over the moduli space of Maslov data. Our primary motivation for this constructio…
Revisiting the Cohen-Jones-Segal construction in Morse-Bott theory
Ciprian Mircea Bonciocat
In 1995, Cohen, Jones and Segal proposed a method of upgrading any given Floer homology to a stable homotopy-valued invariant. For a generic pseudo-gradient Morse-Bott flow on a cl…