Floer homotopy

Author: ostc

August undefined, 2024

WebJan 1, 2009 · In this paper we describe and continue the study begun in Cohen et al. (Progress in Mathematics, vol. 133, Birkhauser, Boston, 1995, pp. 287–325) of the homotopy theory that underlies Floer theory. In that paper the authors addressed the question of realizing a... http://math.columbia.edu/~skr/floer_homotopy_seminar.html

MSRI Floer homotopy theory

WebFloer Homotopy learning seminar, Spring 2024 Seminar on Floer Homotopy Theory This is the webpage of the student learning seminar on Floer Homotopy Theory. The current version of the website design is stolen from the 2024 Seiberg-Witten Seminar. The seminar is usually held on 4:30-6pm in room 507. WebFLOER HOMOTOPY THEORY MSRI / SLMath program August 22 to December 21, 2024 [1] C. Abbas, An introduction to compactness results in symplectic eld theory, Springer, Heidelberg, 2014, ISBN 978-3- ... Floer homology groups in Yang{Mills theory, Cambridge Tracts in Mathematics 147, Cambridge University Press, 2002, ISBN 0-521-80803-0. MR … dictionary\u0027s 8d

Roadmap to Floer homotopy theory? - MathOverflow

WebDec 9, 2024 · Floer homology mirrors the ground-floor theory of homology. But symplectic geometers have long wondered if it’s possible to develop Floer versions of topological theories higher up on the tower: theories that connect the generalized homology with specific features of a space in an infinite-dimensional setting, just as Floer’s original … WebRabinowitz Floer homology, string topology and Floer homotopy theory. It brings together a research cluster and a master-doctorate training program, relying on… Posted Offre publiée il y a plus de 30 jours · plus... WebThis paper is a progress report on our efforts to understand the homotopy theory underlying Floer homology. Its objectives are as follows: (A) to describe some of our ideas concerning what exactly the Floer homology groups compute; (B) to explain what kind of an object we think the «Floer homotopy type» of an infinite dimensional manifold ... dictionary\\u0027s 8d

Floer homology of families I

WebAug 31, 2024 · Given a grid diagram for a knot or link K in , we construct a spectrum whose homology is the knot Floer homology of K. We conjecture that the homotopy type of the spectrum is an invariant of K. Our construction does not use holomorphic geometry, but rather builds on the combinatorial definition of grid homology. city drug store nevisWebFloer homologies are ways of assembling moduli spaces of solutions to certain PDE’s into computable homology-like invariants of certain geometric situations. The … dictionary\\u0027s 8f

"Web44.Periodic Floer pro-spectra from the Seiberg-Witten equations (with P.B. Kronheimer), eprint (2002), arXiv:math/0203243 45.Seiberg-Witten-Floer stable homotopy type of 3-manifolds with b1 = 0, Geometry and Topology 7 (2003), 889–932 Selected Invited Lectures Lecture Series and Mini-courses Aisenstadt Chair lecture series, CRM Montreal ... " - Floer homotopy

Floer homotopy

WebFloer theory of based discsClassical Floer homotopyCurved A1 ring spectra Formulation of Floer homotopy Conjecture Assume that !: ˇ 2(X) !R vanishes (symplectically … Web(Manolescu-Sarkar) A knot Floer stable homotopy type. ArXiv Given a grid diagram for a knot or link K in S3, we construct a spectrum whose homology is the knot Floer homology of K. We conjecture that the homotopy type …

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WebApr 25, 2024 · Abstract: I will introduce the notion of a flow bimodule, and explain. how they give rise to maps between bordism groups of flow categories, which are independent of the bordism type of the bimodule. Then I will. explain the notion of composition of flow bimodules. This leads to a. proof of the invariance of Floer bordism groups under the usual. http://library.msri.org/bib/2024/bib-fhtcnx.pdf

WebJan 24, 2024 · Floer homotopy theory, revisited. In 1995 the author, Jones, and Segal introduced the notion of "Floer homotopy theory". The proposal was to attach a (stable) … WebIn principle, Floer theory can be extended to deﬁne homotopy in-variants of families of equivalent objects (e.g. Hamiltonian isotopic sym-plectomorphisms, 3-manifolds, Legendrian knots, etc.) parametrized by a smooth manifold B. The invariant of a family consists of a ﬁl-tered chain homotopy type, which gives rise to a spectral sequence

WebFeb 27, 2007 · The Floer homotopy type of the cotangent bundle. Let M be a closed, oriented, n-dimensional manifold. In this paper we describe a spectrum in the sense of homotopy theory, Z (T^*M), whose homology is naturally isomorphic to the Floer homology of the cotangent bundle, T^*M. This Floer homology is taken with respect to a … WebJan 20, 2024 · Friday, January 20, 2024 3:00 PM. Ciprian Bonciocat. We will discuss how to exploit the higher-dimensional moduli spaces coming from Morse/Floer theory in order to …

WebSeiberg–Witten–Floer stable homotopy types 891 ikerd∗ ⊕Γ(W 0) ⊂ iΩ1(Y)⊕Γ(W 0),l= ∗d⊕6∂is a linear Fredholm, self-adjoint operator, and cis compact as a map between …

WebIn [6], Cohen, Jones, and Segal posed the question of constructing a \Floer homotopy type." They conjectured that Floer homology (in either of the two variants known at the … city dry cleaners glasgowOne conceivable way to construct a Floer homology theory of some object would be to construct a related spectrum whose ordinary homology is the desired Floer homology. Applying other homology theories to such a spectrum could yield other interesting invariants. This strategy was proposed by Ralph Cohen, John Jones, and Graeme Segal, and carried out in certain cases for Seiberg–Witten–Floer homology by Manolescu (2003) and for the symplectic Floer homology o… dictionary\u0027s 8fWebFeb 3, 2024 · Floer homotopy: theory and practice February 3, 2024 - 04:00 Mohammed Abouzaid, Stanford University McDonnell Hall A02 Register for the Zoom link Morse theory, along with its intimidating infinite dimensional cousin discovered by Floer, has played a fundamental role in developments across topology in the last 50 years. city dry cleaners swanseaWebIn principle, Floer theory can be extended to deﬁne homotopy in-variants of families of equivalent objects (e.g. Hamiltonian isotopic sym-plectomorphisms, 3-manifolds, … dictionary\\u0027s 8jWebDescription. Illustrated by Nathalie Wahl. The development of Floer theory in its early years can be seen as a parallel to the emergence of algebraic topology in the first half of the 20th century, going from counting invariants to homology groups, and beyond that to the … The Mathematical Sciences Research Institute (MSRI), founded in 1982, is an … city dry cleaners camden scWebFloer theory of based discsClassical Floer homotopyCurved A1 ring spectra Formulation of Floer homotopy Conjecture Assume that !: ˇ 2(X) !R vanishes (symplectically aspherical). 1 The moduli spaces of holomorphic discs determine a curved A 1 deformation of 2(X;L) 2 The corresponding category of operadic modules is an invariant of the pair (X;L) up to … dictionary\\u0027s 8kWebA Fleur Homotopy. This will be a hybrid workshop with in-person participation by members of the semester-long program and speakers. Online participation will be open to all who … dictionary\u0027s 8j