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In this article we lay out the details of Fukayas $A_infty$-structure of the Morse complexe of a manifold possibly with boundary. We show that this $A_infty$-structure is homotopically independent of the made choices. We emphasize the transversality arguments that make some fiber products smooth.
In this paper, we study Formans discrete Morse theory in the context of weighted homology. We develop weight
We use rational formality of configuration spaces and the bar construction to study the cohomology of the space of braids in dimension four or greater. We provide a diagram complex for braids and a quasi-isomorphism to the de Rham cochains on the spa
We present a detailed description of a fundamental group algorithm based on Formans combinatorial version of Morse theory. We use this algorithm in a classification problem of prime knots up to 14 crossings.
We construct open book structures on all moment-angle manifolds and describe the topology of their leaves and bindings under certain restrictions. II. We also show, using a recent deep result about contact forms due to Borman, Eliashberg and Murphy [
We prove that Morse local-to-global groups grow exponentially faster than their infinite index stable subgroups. This generalizes a result of Dahmani, Futer, and Wise in the context of quasi-convex subgroups of hyperbolic groups to a broad class of g