More on the degree of a map. Your grade will be determined by your performance on homework assignments and your overall classroom engagement: Here is the Final Exam. Late homeworks will not be accepted. Through this quarter we will construct, prove properties about, and study applications of three such invariants:. Proof of excision via barycentric subdivision, the equivalence of singular and simplicial homology and the 5-lemma. Degrees of maps between spheres.

The fundamental group and the first homology group. Classical applications Brouwer’s fixed point theorem, Jordan-Brouwer curve separation. More on the degree of a map. In addition, students with disabilities should also contact the Office of Disability Services. Towards the homology of CW complexes. Cup product, and the cohomology ring.

Late homeworks will not be accepted.

Homework must be neat, well-organized, and legible. Homework is to be turned in to my office or mailbox by 4: Proof of excision via barycentric subdivision, the equivalence of singular and simplicial homology and the 5-lemma.

## Math 7510: Topology I

The more engaged you are with the material the better. Your grade will gopology determined by your performance on homework assignments and your overall classroom engagement:. It is due on Thursday, November 1, at 5: The homology of real projective space. Classical applications Brouwer’s fixed point theorem, Jordan-Brouwer curve separation.

If you know that there is an impending religious holiday, it is your responsibility to make arrangements to submit homework early.

Immediate applications, including the homology of complex projective spaces. Ralph Cohen Course Assistant. Shoot for lucidity rather than terseness. Students who may need accommodations because of a documented disability should meet with me privately within the first week of classes.

Singular homology, exact sequences and relative homology. Cellular CW homology groups. You are encouraged to discuss problems with each other, but you must work on your own when you write down solutions. Statement zolutions the cohomology ring of projective spaces, an application to the Borsuk-Ulam theorem. Co-chain complexes and cohomology. Homology of good pairs. Use punctuation and conjunctions to indicate your flow of thought rather than arrows or telepathy.

By appointment Homework and Grades: That said, the work you hand in must be your own. Your grade will be determined by your performance on homework assignments and your overall classroom engagement: Degrees of maps between spheres.

# Math A: Algebraic Topology

The Mayer Vietoris sequence. Any cheating during midterms or finals will result in you failing the exam. The fundamental group and the first homology group.

In addition, students with disabilities should also contact the Office of Disability Services.

The Universal Coefficient Theorem continued. Here is the midterm exam. Solutjons your handwriting is difficult to read, type your homework. Allen Hatcher’s Algebraic Topologyavailable for free download here. A basic class of topological spaces we will apply our discussion to is the class of CW complexes.

As a necessary ingredient, we will develop techniques in homological algebra.