Studies regular and critical values, gradient flow, handle decompositions, Morse theory, h-cobordism theorem, Dehn's lemma in dimension 3, and disk theorem in dimension 4. Prerequisite: Math 5770.
Graduate Course Descriptions
Topology of Manifolds (3.00)
MATH 8750
Generalized Cohomology Theory (3.00)
MATH 8800
Topics include the axiomatic generalized cohomology theory; representability and spectra; spectra and ring spectra; orientability of bundles in generalized cohomology theory; Adams spectral sequence, and stable homotopy.
Cobordism and K-Theory (3.00)
MATH 8830
Studies classical cobordism theories; Pontryagin-Thom construction; bordism and cobordism of spaces; K-theory and Bott periodicity; formal groups, and cobordism.
Topics in Algebraic Topology (3.00)
MATH 8850
Selected advanced topics in algebraic topology.
Group Theory (3.00)
MATH 8851
Studies the basic structure theory of groups, especially finite groups.
Representation Theory (3.00)
MATH 8852
Studies the foundations of representation and character theory of finite groups.
Algebraic Combinatorics (3.00)
MATH 8853
Studies geometries, generating functions, partitions, and error-correcting codes and graphs using algebraic methods involving group theory, number theory, and linear algebra.
Arithmetic Groups (3.00)
MATH 8854
General methods of analyzing groups viewed as discrete subgroups of real algebraic subgroups. Additional topics include the congruence subgroup problem. Prerequisite: MATH 7752.
Theory of Algebras (3.00)
MATH 8855
Studies the basic structure theory of associative or nonassociative algebras.
Transformation Groups (3.00)
MATH 8880
Studies groups of transformations operating on a space; properties of fixed-point sets, orbit spaces; and local and global invariants.
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