Floer homotopy

Author: xipb

August undefined, 2024

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 ... 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 …

Floer Homotopy of Lagrangian Submanifolds - Columbia …

WebChromatic homotopy theory provides an effective way to understand stable homotopy groups of spheres. More recently, geometric topologists also arise interest in it because … http://math.columbia.edu/~skr/floer_homotopy_seminar.html periodization macro and micro training cycles

Floer Homotopy of Lagrangian Submanifolds

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 … WebFLOER HOMOTOPY THEORY Connections Workshop MSRI / SLMath September 8 to 9, 2024 Books [1] D. Barnes and C. Roitzheim, Foundations of stable homotopy theory, … periodization strength training program pdf

[2108.13566] A knot Floer stable homotopy type - arXiv

WebFloer 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 … WebFloer homologies are ways of assembling moduli spaces of solutions to certain PDE’s into computable homology-like invariants of certain geometric situations. The … periodization methodWebJul 11, 2024 · The idea of stable homotopy refinements of Floer homology was first introduced by Cohen, Jones, and Segal in a 1994 paper, but it was only in the last … periodization theory and method of training

"WebAn Introduction to Symplectic Geometry for Lagrangian Floer Homology. Expository master’s thesis (2024) written as part of my Ph.D. qualifying exam, supervised by Prof. Jonathan Block. This thesis introduces symplectic geometry with an eye towards developing Floer homology for Lagrangian intersections. " - Floer homotopy

Floer homotopy

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 … WebJun 7, 2024 · Recently I became intrigued by Floer homotopy, especially after seeing it had been applied to classical questions in symplectic topology. (e.g. Abouzaid and Kragh). This revelation made me excited about the new possibilities that this approach opens up, and I want to try and find other applications.

Did you know?

One 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… 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.

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. WebFloer theory of based discsClassical Floer homotopyCurved A1 ring spectra Formulation of Floer homotopy Conjecture Assume that !: ˇ 2(X) !R vanishes (symplectically …

WebSeminar 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 … 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...

WebAug 31, 2024 · A knot Floer stable homotopy type. 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 …

http://math.columbia.edu/~skr/floer_homotopy_seminar.html periodization training bookWebSymplectic Topology and Floer Homology Volume 2 Published in two volumes, this is the ﬁrst book to provide a thorough and systematic explanation of symplectic topology, and the analytical details and techniques used in ... Simpson Homotopy Theory of Higher Categories 20. E. Fricain and J. Mashreghi The Theory of H(b) Spaces I periodization training cyclingWebIn [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 … periodization training for runnersWebDescription. 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 … periodization training for elite sprintersWebThis 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 … periodization training for sports 3rd editionWebFeb 9, 2024 · Floer homotopy: theory and practice. Morse theory, along with its intimidating infinite dimensional cousin discovered by Floer, has played a … periodization training for endurance athletesWebThe stable homotopy type SWF((2 ;3;11)) is that of the unreduced suspension of Pin(2), with one of the cone points as the basepoint, and with the induced Pin(2)-action. 3.5. Properties. Let us now describe a few properties of Seiberg-Witten Floer homologies and stable homotopy types. We will omit the Spincstructures from notation for simplicity ... periodization training for running