## MATH 583, Spring 2013

Course Title: Introduction to K-Theory

Instructor: Nigel Higson

Class Meeting Times: Mondays, Wednesdays and Fridays, 12:20-1:10 in 113 McAllister

Office Hours: By appointment

Overview: The goal of the course is to introduce topological K-theory and present some of its applications, and then explain the extension of topological K-theory to C*-algebras. High points will be the Bott periodicity theorem, the application of topological K-theory to the Hopf invariant one problem, and the application of C*-algebra K-theory to the study of noncommutative tori. Prerequisites include basic familiarity with general topology, linear algebra and functional analysis (roughly as in the first year graduate courses). From time to time further background material will be assumed (for example aspects of manifold theory), but also reviewed in class.

Piazza: I’ve set up a piazza.com page for the course. Students, you’ll need to send me your email address to obtain access.

Class Work: I’ll provide a variety of homework problems that I hope will help deepen our understanding of the material. These will form the basis for discussion on piazza. There will be no exams.

Text: I recommend Hatcher’s online text for the first parts of the course. After that I’ll supply lecture notes for at least some of the C*-topics.

Academic Integrity: Students must adhere to the University's and the College's standards of academic integrity. The University defines academic integrity as "the pursuit of scholarly activity in an open, honest, and responsible manner." It further states that "Academic integrity includes a commitment not to engage in or tolerate acts of falsification, misrepresentation or deception. Such acts of dishonesty violate the fundamental ethical principles of the University community and compromise the worth of work completed by others." See this page for more information about the University and College academic integrity policies. For a more compelling account of what honesty and integrity mean for a scientist (or a mathematician), read this famous speech by Richard Feynman.

Disability Statement: Penn State welcomes students with disabilities into the University's educational programs. If you have a disability-related need for reasonable academic adjustments in this course, contact the Office for Disability Services (ODS) at 814-863-1807 (V/TTY). For further information regarding ODS, please visit the Office for Disability Services Web site at http://equity.psu.edu/ods/. In order to receive consideration for course accommodations, you must contact ODS and provide documentation (see the documentation guidelines at http://equity.psu.edu/ods/guidelines/documentation-guidelines). If the documentation supports the need for academic adjustments, ODS will provide a letter identifying appropriate academic adjustments. Please share this letter and discuss the adjustments with your instructor as early in the course as possible. You must contact ODS and request academic adjustment letters at the beginning of each semester.

Instructor: Nigel Higson

Class Meeting Times: Mondays, Wednesdays and Fridays, 12:20-1:10 in 113 McAllister

Office Hours: By appointment

Overview: The goal of the course is to introduce topological K-theory and present some of its applications, and then explain the extension of topological K-theory to C*-algebras. High points will be the Bott periodicity theorem, the application of topological K-theory to the Hopf invariant one problem, and the application of C*-algebra K-theory to the study of noncommutative tori. Prerequisites include basic familiarity with general topology, linear algebra and functional analysis (roughly as in the first year graduate courses). From time to time further background material will be assumed (for example aspects of manifold theory), but also reviewed in class.

Piazza: I’ve set up a piazza.com page for the course. Students, you’ll need to send me your email address to obtain access.

Class Work: I’ll provide a variety of homework problems that I hope will help deepen our understanding of the material. These will form the basis for discussion on piazza. There will be no exams.

Text: I recommend Hatcher’s online text for the first parts of the course. After that I’ll supply lecture notes for at least some of the C*-topics.

Academic Integrity: Students must adhere to the University's and the College's standards of academic integrity. The University defines academic integrity as "the pursuit of scholarly activity in an open, honest, and responsible manner." It further states that "Academic integrity includes a commitment not to engage in or tolerate acts of falsification, misrepresentation or deception. Such acts of dishonesty violate the fundamental ethical principles of the University community and compromise the worth of work completed by others." See this page for more information about the University and College academic integrity policies. For a more compelling account of what honesty and integrity mean for a scientist (or a mathematician), read this famous speech by Richard Feynman.

Disability Statement: Penn State welcomes students with disabilities into the University's educational programs. If you have a disability-related need for reasonable academic adjustments in this course, contact the Office for Disability Services (ODS) at 814-863-1807 (V/TTY). For further information regarding ODS, please visit the Office for Disability Services Web site at http://equity.psu.edu/ods/. In order to receive consideration for course accommodations, you must contact ODS and provide documentation (see the documentation guidelines at http://equity.psu.edu/ods/guidelines/documentation-guidelines). If the documentation supports the need for academic adjustments, ODS will provide a letter identifying appropriate academic adjustments. Please share this letter and discuss the adjustments with your instructor as early in the course as possible. You must contact ODS and request academic adjustment letters at the beginning of each semester.