Floer homology

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Related lectures (32)

Homology and the fundamental group

Explores simplicial and singular homology, reduced homology groups, and their connection to the fundamental group.

Smooth maps and differentials: Smooth maps

Explores smooth maps between submanifolds, discussing smoothness criteria and composition preservation.

Induced Homomorphisms

Covers induced homomorphisms, homotopy invariance, and homology groups of quotients.

A Lemma: Introduction to Homology Groups

Introduces the concept of homology groups and focuses on a lemma about free abelian groups.

Homology of Riemann Surfaces

Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.

Smith Theory in Floer Persistence and Dynamics

Covers Smith theory in Floer persistence and dynamics, exploring classical mechanics invariants, Poincaré-Birkhoff theorem, and the Hofer-Zehnder conjecture.

Introduction to Topology

Covers fundamental concepts of space, topology, groups, and homology theory.

Homology with coefficients

Covers homology with coefficients, introducing the concept of defining homology groups with respect to arbitrary abelian groups.

Cup and Cap Product: Poincaré Duality

Explains the cup and cap product in algebraic topology and their relation to homology groups.

Homology Theorem

Covers the proof of Theorem A, discussing homology, quotients, and isomorphisms.

Cellular Homology

Explains cellular homology and the computation of homology groups using boundary maps.

Functors: Assigning Morphisms and Dual Spaces

Covers the concept of functors, assigning morphisms and dual spaces in different categories.

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