Combinatorial Floer homology by Vin De Silva, Joel W. Robbin, Dietmar A. Salamon

By Vin De Silva, Joel W. Robbin, Dietmar A. Salamon

The authors outline combinatorial Floer homology of a transverse pair of noncontractible nonisotopic embedded loops in an orientated 2 -manifold with out boundary, turn out that it truly is invariant lower than isotopy, and end up that it truly is isomorphic to the unique Lagrangian Floer homology. Their facts makes use of a formulation for the Viterbo-Maslov index for a tender lune in a 2 -manifold

Show description

Read or Download Combinatorial Floer homology PDF

Similar topology books

Infinite words : automata, semigroups, logic and games

Countless phrases is a vital conception in either arithmetic and laptop Sciences. Many new advancements were made within the box, inspired via its program to difficulties in computing device technology. countless phrases is the 1st guide dedicated to this subject. limitless phrases explores all facets of the idea, together with Automata, Semigroups, Topology, video games, common sense, Bi-infinite phrases, endless bushes and Finite phrases.

Topological Vector Spaces

The current booklet is meant to be a scientific textual content on topological vector areas and presupposes familiarity with the weather of basic topology and linear algebra. the writer has came upon it pointless to rederive those effects, considering that they're both easy for plenty of different components of arithmetic, and each starting graduate pupil is probably going to have made their acquaintance.

Hamiltonian Dynamics and Celestial Mechanics: A Joint Summer Research Conference on Hamiltonian Dynamics and Celestial Mechanics June 25-29, 1995 Seattle, Washington

This ebook comprises chosen papers from the AMS-IMS-SIAM Joint summer time examine convention on Hamiltonian structures and Celestial Mechanics held in Seattle in June 1995.

The symbiotic dating of those issues creates a normal blend for a convention on dynamics. subject matters lined contain twist maps, the Aubrey-Mather concept, Arnold diffusion, qualitative and topological reviews of structures, and variational tools, in addition to particular subject matters resembling Melnikov's approach and the singularity homes of specific systems.

As one of many few books that addresses either Hamiltonian structures and celestial mechanics, this quantity deals emphasis on new concerns and unsolved difficulties. some of the papers supply new effects, but the editors purposely incorporated a few exploratory papers in line with numerical computations, a piece on unsolved difficulties, and papers that pose conjectures whereas constructing what's known.


Open study problems
Papers on important configurations

Readership: Graduate scholars, learn mathematicians, and physicists drawn to dynamical structures, Hamiltonian structures, celestial mechanics, and/or mathematical astronomy.

Extra info for Combinatorial Floer homology

Example text

If Λ satisfies the arc condition then g A ∩ A = ∅ and g B ∩ B = ∅ for every g ∈ Γ \ {id}. In particular, for every g ∈ Γ \ {id}, we have gx, gy ∈ / A∪B and hence (21) holds by (i). 2 that the cancellation formula (20) holds for every g ∈ Γ \ {id}. 4. The next lemma deals with (α, β)-traces connecting a point x ∈ α ∩ β to itself. An example on the annulus is depicted in Figure 5. 5 (Isotopy Argument). Suppose Σ is not diffeomorphic to the 2sphere. 1. Suppose that there is a deck transformation g0 ∈ Γ \ {id} such that y = g0 x.

Then εx = −1 and εy = 1.

Hence 0 = μ(Λ0 ) − μ(Λ) = = mx0 (Λ0 ) + my0 (Λ0 ) mx (Λ) + my (Λ) − 2 2 1 mgk x (Λ) + mg−k y (Λ) 2 k=0 = mgx (Λ) + mg−1 y (Λ). Here the last equation follows from (21). 2. 3. Suppose Σ is not diffeomorphic to the 2-sphere. 1 and denote να := ∂ w|α\β and νβ := −∂ w|β\α . Choose smooth paths γα : [0, 1] → α, γβ : [0, 1] → β from γα (0) = γβ (0) = x to γα (1) = γβ (1) = y such that γα is an immersion when να ≡ 0 and constant when να ≡ 0, the same holds for γβ , and να (z) = deg(γα , z) for z ∈ α \ {x, y}, νβ (z) = deg(γβ , z) for z ∈ β \ {x, y}.

Download PDF sample

Rated 4.19 of 5 – based on 43 votes