Algebraic Topology Notes: Homotopy Theory
نویسنده
چکیده
Notes on homotopy theory, the first part of a trilogy on algebraic topology. Any typos, errors, mistakes, gaffes, etc., are entirely my folly.
منابع مشابه
Notes for second semester algebraic topology
These are some notes for a second-semester algebraic topology course at UC Berkeley which I taught in 2004 and 2005. The topics of the course are: higher homotopy groups and obstruction theory, bundles and characteristic classes, spectral sequences, and Morse theory and applications to differential topology. Disclaimers: These notes are intended as an elementary introduction to selected core id...
متن کاملIntroduction to Combinatorial Homotopy Theory
1 Introduction. Homotopy theory is a subdomain of topology where, instead of considering the category of topological spaces and continuous maps, you prefer to consider as morphisms only the continuous maps up to homotopy, a notion precisely defined in these notes in Section 4. Roughly speaking, you decide not to distinguish two maps which can be continuously deformed into each other; such a wea...
متن کاملM392c Notes: a Course on Seiberg-witten Theory and 4-manifold Topology
1. Classification problems in differential topology: 1/18/18 1 2. Review of the algebraic topology of manifolds: 1/23/18 4 3. Unimodular forms: 1/25/18 8 4. The intersection form and characteristic classes: 1/30/18 12 5. Tangent bundles of 4-manifolds: 2/1/18 16 6. Rokhlin’s theorem and the homotopy theorem: 2/6/18 19 7. The homotopy theorem: 2/8/18 22 8. The Hodge star: 2/13/18 22 9. Hodge the...
متن کاملIntroduction to higher homotopy groups and obstruction theory
These are some notes to accompany the beginning of a secondsemester algebraic topology course. The goal is to introduce homotopy groups and their uses, and at the same time to prepare a bit for the study of characteristic classes which will come next. These notes are not intended to be a comprehensive reference (most of this material is covered in much greater depth and generality in a number o...
متن کاملMorse theory, graphs, and string topology
In these lecture notes we discuss a body of work in which Morse theory is used to construct various homology and cohomology operations. In the classical setting of algebraic topology this is done by constructing a moduli space of graph flows, using homotopy theoretic methods to construct a virtual fundamental class, and evaluating cohomology classes on this fundamental class. By using similar c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011