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INTRODUCTORY TOPOLOGY II

MATH 752
과목 설명

Continuation ofMATH 751. Cohomology, Universal Coefficient Theorem, Kunneth Formula, cup and cap products, applications to manifolds, orientability, Poincare Duality. Differential forms, integration and Stokes Theorem, De Rham Theorem. Calculations, further duality theorems, Euler class, Lefschetz Fixed-Point Theorem.

선수과목

Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program

충족 요건

This course does not satisfy any prerequisites.

학점

미보고

개설 시기

미보고

평점
3.63

-4.65% 과거 데이터 대비

수료율
100%

0.87% 과거 데이터 대비

A 비율
68.75%

-13.32% 과거 데이터 대비

학급 규모
16

17.24% 과거 데이터 대비

Cumulative Grade Distribution

강사 (2026 Summr)

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유사 과목

INTRODUCTORY TOPOLOGY I

MATH 751

An introduction to algebraic and differential topology. Elements of homotopy theory, fundamental group, covering spaces. Differentiable manifolds, tangent vectors, regular values, transversality, examples of compact Lie groups. Homological algebra, chain complexes, cell complexes, singular and cellular homology, calculations for surfaces, spheres, projective spaces, etc. Familiarity with undergraduate algebra and topologyMATH 541or551) is strongly recommended.

ELEMENTARY GEOMETRIC AND ALGEBRAIC TOPOLOGY

MATH 552

Introduction to algebraic topology. Emphasis on geometric aspects, including two-dimensional manifolds, the fundamental group, covering spaces, basic simplicial homology theory, the Euler-Poincare formula, and homotopy classes of mappings.

TOPICS IN DIFFERENTIAL TOPOLOGY

MATH 856

The theory of differential manifolds such as differential forms and de Rham theorem, cobordism groups, Lie groups, homogeneous spaces, fiber bundles, characteristic classes.

TOPICS IN GEOMETRIC TOPOLOGY

MATH 851

Advanced Topics in Geometric Topology.

ALGEBRAIC TOPOLOGY I

MATH 753

Higher homotopy groups, elements of obstruction theory, fibrations, bundle theory, classifying spaces, applications to smooth mainfolds, differential forms, vector bundles, characteristic classes, cobordism, applications and calculations. Basic graduate topology courses (e.g.MATH 751and752) are strongly recommended.