Do you want to publish a course? Click here

A sheaf-theoretic model for SL(2,C) Floer homology

102   0   0.0 ( 0 )
 Added by Ciprian Manolescu
 Publication date 2017
  fields
and research's language is English




Ask ChatGPT about the research

Given a Heegaard splitting of a three-manifold Y, we consider the SL(2,C) character variety of the Heegaard surface, and two complex Lagrangians associated to the handlebodies. We focus on the smooth open subset corresponding to irreducible representations. On that subset, the intersection of the Lagrangians is an oriented d-critical locus in the sense of Joyce. Bussi associates to such an intersection a perverse sheaf of vanishing cycles. We prove that in our setting, the perverse sheaf is an invariant of Y, i.e., it is independent of the Heegaard splitting. The hypercohomology of this sheaf can be viewed as a model for (the dual of) SL(2,C) instanton Floer homology. We also present a framed version of this construction, which takes into account reducible representations. We give explicit computations for lens spaces and Brieskorn spheres, and discuss the connection to the Kapustin-Witten equations and Khovanov homology.



rate research

Read More

Area-preserving diffeomorphisms of a 2-disc can be regarded as time-1 maps of (non-autonomous) Hamiltonian flows on solid tori, periodic flow-lines of which define braid (conjugacy) classes, up to full twists. We examine the dynamics relative to such braid classes and define a braid Floer homology. This refinement of the Floer homology originally used for the Arnold Conjecture yields a Morse-type forcing theory for periodic points of area-preserving diffeomorphisms of the 2-disc based on braiding. Contributions of this paper include (1) a monotonicity lemma for the behavior of the nonlinear Cauchy-Riemann equations with respect to algebraic lengths of braids; (2) establishment of the topological invariance of the resulting braid Floer homology; (3) a shift theorem describing the effect of twisting braids in terms of shifting the braid Floer homology; (4) computation of examples; and (5) a forcing theorem for the dynamics of Hamiltonian disc maps based on braid Floer homology.
We study possible configurations of singular points occuring on general algebraic curves in $mathbb{C}P^2$ via Floer theory. To achieve this, we describe a general formula for the $H_{1}$-action on the knot Floer complex of the knotification of a link in $S^3$, in terms of natural actions on the link Floer complex of the original link. This result may be interest on its own.
We develop a skein exact sequence for knot Floer homology, involving singular knots. This leads to an explicit, algebraic description of knot Floer homology in terms of a braid projection of the knot.
200 - Benjamin Audoux 2017
We define a grid presentation for singular links i.e. links with a finite number of rigid transverse double points. Then we use it to generalize link Floer homology to singular links. Besides the consistency of its definition, we prove that this homology is acyclic under some conditions which naturally make its Euler characteristic vanish.
comments
Fetching comments Fetching comments
Sign in to be able to follow your search criteria
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا