Math-142 Elementary Algebraic Topology

Math-142 Elementary Algebraic Topology, Fall 2019

Lectures: Mon.-Wed.-Fri. 10:00AM-11:00AM (Berkeley Time) at Cory 247

Professor: Semeon Artamonov

Textbook: M.A.Armstrong "Basic Topology" (You can download textbook for free on campus via SpringerLink)

Office Hours: Mon.-Wed.-Fri. 11:30AM-12:30PM (or by Appointment) at 1055 Evans Hall

Syllabus

Homework Assignments

Due Sep 9: Chapter 1: 1, Problems A,B (by the link), 8, 11, 14, 22, 26
Due Sep 13: Chapter 2: 1, 2, 9, 18, Problems A,B,C,D (by the link)
Due Sep 20: Chapter 3: 5, 9, 12, 15, 17, 20, Problems A,B (by the link)
Due Sep 27: Chapter 3: 25, 31, 35, Problems A,B (by the link), 37, 41; Chapter 4: 3, 6
Due Oct 4: Chapter 4: 17, 19, 23, 24, 29, 30, 32
Due Oct 18: Chapter 5: 6, 7, 10, 11
Due Oct 30: Chapter 5: 22, 24, 25, 26, 29, Problem A (by the link)
Due Nov. 6: Chapter 6: 1, 3, 5, 9, 17, Problem A (by the link)
Due Nov. 13: Problem A (by the link), Chapter 7: 3, 4
Due Dec. 2: Chapter 7: 17, 27, 28, 29, 30; Chapter 8: 10, 11, 13

Reading Assignments

Wed, Aug. 28	Introduction to Topological Equivalence and Topological Invariants	§1.1, §1.2, §1.6
Fri, Aug. 30	Surfaces and Abstract Spaces	§1.3, §1.4, §1.5
Mon, Sep. 2	No Class, Holiday
Wed, Sep. 4	Topological Spaces	§2.1
Fri, Sep. 6	Continuous Functions	§2.2; §2.3
Mon, Sep. 9	Compact spaces	§3.1,3.2
Wed, Sep. 11	Hausdorff spaces	§ 3.3
Fri, Sep. 13	Product spaces	§ 3.4
Mon, Sep. 16	Connected Spaces	§ 3.5
Wed, Sep. 18	Path-Connected Spaces	§ 3.6
Fri, Sep. 20	Identification Topology	§ 4.1; §4.2
Mon, Sep. 23	Identification Topology (continued)	§ 4.2
Wed, Sep. 25	Topological Groups	§ 4.3
Fri, Sep. 27	Orbit Spaces	§ 4.4
Mon, Sep. 30	Homotopic Maps	§ 5.1
Wed, Oct. 2	Fundamental Group	§ 5.2
Fri, Oct. 4	Midterm I
Mon, Oct. 7	Basic Properties of the Fundamental Group	§5.2; §5.3
Wed, Oct. 9	Class cancelled due to power outage
Fri, Oct. 11	Class cancelled due to power outage
Mon, Oct. 14	Calculations of simplest fundamental Groups	§5.3
Wed, Oct. 16	Path-lifting and Homotopy-lifting for S^1	§5.3
Fri, Oct. 18	Covering spaces and Homotopy Type	§5.3; §5.4
Mon, Oct. 21	Homotopy Type (continued)	§5.4
Wed, Oct. 23	Triangulations	§6.1
Fri, Oct. 25	Barycentric subdivision and Simplicial Approximation	§6.2; §6.3
Mon, Oct. 28	Class cancelled due to power outage
Wed, Oct. 30	Simplicial Approximation Theorem	§6.3
Fri, Nov. 1	Edge Group of a Complex	§6.4
Mon, Nov. 4	Van Kampen Theorem	§6.4
Wed, Nov. 6	Manifolds and Surfaces	§7.1
Fri, Nov. 8	Triangulation and Orientation of Surfaces	§7.2
Mon, Nov. 11	No Class, Holiday
Wed, Nov. 13	Midterm II
Fri, Nov. 15	Euler Characteristic and Surgery	§7.3; §7.4
Mon, Nov. 18	Surface Symbols	§7.5
Wed, Nov. 20	Cycles and Boundaries	§8.1
Fri, Nov. 22	Chains and Homology Groups	§8.2
Mon, Nov. 25	Calculations of Simplest Homology Groups	§8.3
Wed, Nov. 27	No Class, Holiday
Fri, Nov. 29	No Class, Holiday
Mon, Dec. 2	Simplicial Maps	§8.4
Wed, Dec. 4	Stellar subdivision	§8.5
Fri, Dec. 6	Homotopy invariance	§8.6