Math 109a  
Geometry and Topology 

Fall 201112  

Instructor: Susama Agarwala, Sloan 276, 6263954347, susama@caltech.edu Grader: Edward Fan, Sloan 155,
sfan@caltech.edu 


Instructor office hours for the week of September 3 moved to Tuesday September 4, 13 pm. Midterm due date: Wednessday Oct 26 On the week of the 17th, I will spend October 19th answering any questions on the point set topology material we have covered. If there are more questions than class time allows, I will continue answering questions after class or by appointment. If there are not many questions, I will start on Homotopy theory. In homework 3, problem 1, the space X is the disjoint union of two copies of the real line, and the topology is defined accordingly. OCT 21, 3:15 PM. MIDTERM CORRECTION! Problem 3 on the midterm has been updated. Please make sure you have printed a recent version. Nov 22 Homework 8 Due on Friday Dec 2 Nov 30 Review session in class on Friday, December 2. Please email me any exercises that you want me to do in class by Thursday 5 pm. 


Math 109a is the first course in the math 109 sequence, Introduction to Geometry and Topology. In the first part of the course, we will develop ideas from general topology. This will include the definition of topological spaces and basic examples and constructions. We will study properties of spaces including connectedness and compactness, and we will briefly discuss the difficulties that can arise in general topological spaces. In the remainder of the course, we will introduce some invariants from algebraic topology, including the fundamental group of a space and the homology groups of a space. We will discuss some preliminary concepts from group theory, including group presentations, and prove Van Kampen's theorem, which makes it possible to compute fundamental groups. We will study the simplicial and singular versions of homology theory. We will consider many examples. 

Prerequisites: Ma 2 or equivalent, and Ma 108 must be taken previously or concurrently. Grading Policy: Class participation 10%, homework 30%, midterm 30% and final exam 30 %. The class participation grade includes but is not limited to attendance, questions asked in class, outside of class, or in TA and instructors office hours. Homework Policy: Homework is due at 1 p.m. sharp on Wednesdays, in the box for Ma 109 in the hallway outside the math office (Sloan 253). Each student is allowed one late homework, at the instructor's discretion. The instructor should be notified of the extension request at least 24 hours before the homework is due. 

We will use "Topology" , James Munkres, PrenticeHall, 2000. as a reference for the first part of the course. We will use Hatcher's "Algebraic Topology" (available at the author's webpage) as the textbook for the material in the second part of the course. 






