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Friday, October 4, 2013 - 14:00 ,
Location: Skiles 006 ,
John Etnyre ,
Georgia Tech ,
Organizer: John Etnyre

Gabai has a nice criteria for recognizing fibered knots in 3-manifolds. This criteria is best described in terms of sutured manifolds and simple sutured hierarchies. We will introduce this terminology and prove Gabai's result. Given time (or in subsequent talks) we might discuss generalizations concerning constructing foliations on knot compliments and 3-manifolds in general. Such results are very useful in understanding the minimal genus representatives of homology classes in the manifold (in particular, the minimal genus of a Seifert surface for a knot).

Friday, September 27, 2013 - 14:00 ,
Location: Skiles 006 ,
None ,
None ,
Organizer: John Etnyre

No talk today. Ga Tech will be hosting a prospective graduate students day for undergraduates in the Georgia area.

Friday, September 20, 2013 - 14:00 ,
Location: Skiles 006 ,
Kirsten Wickelgren ,
Georgia Tech ,
Organizer: John Etnyre

Allowing formal desuspensions of maps and objects takes the category of topological spaces to the category of spectra, where cohomology is naturally represented. The EHP spectral sequence encodes how far one can desuspend maps between spheres. It's among the most useful tools for computing homotopy groups of spheres. RP^infty has a cell structure with a cell in each dimension and with attaching maps of degrees ...020202... Note that this sequence is periodic. In fact, it is more than the degrees of these maps which are periodic and a map of Snaith relates this periodicity to the EHP sequence.We will develop the EHP sequence, James periodicity and the relationship between the two.

Friday, September 13, 2013 - 14:00 ,
Location: Skiles 006 ,
Kirsten Wickelgren ,
Georgia Tech ,
Organizer: John Etnyre
Allowing formal desuspensions of maps and objects takes the category of topological spaces to the category of spectra, where cohomology is naturally represented. The EHP spectral sequence encodes how far one can desuspend maps between spheres. It's among the most useful tools for computing homotopy groups of spheres. RP^infty has a cell structure with a cell in each dimension and with attaching maps of degrees ...020202... Note that this sequence is periodic. In fact, it is more than the degrees of these maps which are periodic and a map of Snaith relates this periodicity to the EHP sequence.We will develop the EHP sequence, James periodicity and the relationship between the two.

Note this is a 1 hour seminar (not the usual 2 hours).

Friday, September 6, 2013 - 14:00 ,
Location: Skiles 006 ,
Kirsten Wickelgren ,
Georgia Tech ,
Organizer: John Etnyre
Allowing formal desuspensions of maps and objects takes the category of topological spaces to the category of spectra, where cohomology is naturally represented. The EHP spectral sequence encodes how far one can desuspend maps between spheres. It's among the most useful tools for computing homotopy groups of spheres. RP^infty has a cell structure with a cell in each dimension and with attaching maps of degrees ...020202... Note that this sequence is periodic. In fact, it is more than the degrees of these maps which are periodic and a map of Snaith relates this periodicity to the EHP sequence.We will develop the EHP sequence, James periodicity and the relationship between the two.

Note this is a 1 hour seminar (not the usual 2 hours).

Friday, April 26, 2013 - 11:30 ,
Location: Skiles 006 ,
John Etnyre ,
Georgia Tech ,
Organizer: John Etnyre

In this series of talks I will begin by discussing the idea of studying smooth manifolds and their submanifolds using the symplectic (and contact) geometry of their cotangent bundles. I will then discuss Legendrian contact homology, a powerful invariant of Legendrian submanifolds of contact manifolds. After discussing the theory of contact homology, examples and useful computational techniques, I will combine this with the conormal discussion to define Knot Contact Homology and discuss its many wonders properties and conjectures concerning its connection to other invariants of knots in S^3.

Friday, April 19, 2013 - 12:05 ,
Location: Skiles 006 ,
John Etnyre ,
Georgia Tech ,
Organizer: John Etnyre
In this series of talks I will begin by discussing the idea of studying smooth manifolds and their submanifolds using the symplectic (and contact) geometry of their cotangent bundles. I will then discuss Legendrian contact homology, a powerful invariant of Legendrian submanifolds of contact manifolds. After discussing the theory of contact homology, examples and useful computational techniques, I will combine this with the conormal discussion to define Knot Contact Homology and discuss its many wonders properties and conjectures concerning its connection to other invariants of knots in S^3.

Friday, April 5, 2013 - 11:30 ,
Location: Skiles 006 ,
John Etnyre ,
Georgia Tech ,
Organizer: John Etnyre
In this series of talks I will begin by discussing the idea of studying smooth manifolds and their submanifolds using the symplectic (and contact) geometry of their cotangent bundles. I will then discuss Legendrian contact homology, a powerful invariant of Legendrian submanifolds of contact manifolds. After discussing the theory of contact homology, examples and useful computational techniques, I will combine this with the conormal discussion to define Knot Contact Homology and discuss its many wonders properties and conjectures concerning its connection to other invariants of knots in S^3.

Friday, March 1, 2013 - 11:30 ,
Location: Skiles 006 ,
John Etnyre ,
Ga Tech ,
Organizer: John Etnyre
In this series of talks I will begin by discussing the idea of studying smooth manifolds and their submanifolds using the symplectic (and contact) geometry of their cotangent bundles. I will then discuss Legendrian contact homology, a powerful invariant of Legendrian submanifolds of contact manifolds. After discussing the theory of contact homology, examples and useful computational techniques, I will combine this with the conormal discussion to define Knot Contact Homology and discuss its many wonders properties and conjectures concerning its connection to other invariants of knots in S^3.

Friday, February 22, 2013 - 11:30 ,
Location: Skiles 006 ,
John Etnyre ,
Ga Tech ,
Organizer: John Etnyre
In this series of talks I will begin by discussing the idea of studying smooth manifolds and their submanifolds using the symplectic (and contact) geometry of their cotangent bundles. I will then discuss Legendrian contact homology, a powerful invariant of Legendrian submanifolds of contact manifolds. After discussing the theory of contact homology, examples and useful computational techniques, I will combine this with the conormal discussion to define Knot Contact Homology and discuss its many wonders properties and conjectures concerning its connection to other invariants of knots in S^3.