Topology and Geometry Homework Help

Topology and Geometry can be put under single umbrella where topology is the modern version of geometry. Geometry is study of shape and figure whereas Topology is study of space.  Students study  free quantum theories, classical field theory and Feynman diagrams; metrization theorems, function spaces,  topological spaces and continuous functions, embedding theorems, connectedness, compactness, separation axioms;  concrete aspects of geometry, centered on the notion of curvature; Dirac geometry(developed by Courant), complex geometry Weinstein, and Severa; spinors , tensors, Hilbert space,  Group theory,  linear algebra;  complex algebraic varieties and complex analytic varieties; surfaces (Bombieri-Mumford for characteristic p, Enriques-Castelnuovo for characteristic zero); cohomology theory and homology, including cup products, intersection pairings, and the Lefschetz fixed point theorem, Kunneth formulas;  Lie groups, the de Rham theorem, and Riemannian manifolds, differentiable manifolds and vector fields and forms topics under Geometry and Topology in their academics.

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