Wednesday, April 18, 2018
4:20 PM - 5:20 PM (ET)
Exley Science Center Tower ESC 638
Event Type
Seminar/Colloquium
Contact
Canalia, Caryn
2182
Link
https://eaglet.wesleyan.edu/MasterCalendar/EventDetails.aspx?EventDetailId=79043
Melissa
Zhang, Boston College
Symmetries in topological spaces and homology-type invariants
Abstract: Topologists
often encounter spaces with interesting symmetries. By analyzing the symmetries
of an object through the regularities of its algebraic invariants, we are able
to learn more about the object and its relationship with smaller, less complex
objects. For example, by using the right tools, we can easily see that for a
topological space X equipped with a cyclic action, the rank of the
singular homology of X is at least that of the fixed point set.
In low-dimensional topology, knots and links are ubiquitous and far-reaching in
their associations. One particular interesting algebraic invariant of links is
Khovanov homology, a combinatorial homology theory whose graded Euler
characteristic is the Jones polynomial. In this talk, we consider links
exhibiting 2-fold symmetry and prove a rank inequality for a variant of
Khovanov homology.