Date & Time: Tuesday, September 09, 2014, 16:00-17:00.
Venue: Ramanujan Hall
Title: Twisted Homology - With Applications to Ring Spectra
Speaker: Samik Basu, RKM Vivekananda University
Abstract: For a generalised cohomology theory (which has a commutative graded ring structure) $ R $, one considers the functor which takes a space to the units in the $0^{th} $ graded piece. This functor can be written as homotopy classes of maps to some topological space, which we write as $ GL_1R $, and thus, the action of units on the cohomology ring equips $ R $ with a topological $ GL_1R $-action. As a consequence a $ 1 $-cocycle with values in $ GL_1R $ gives us new homology and cohomology theories which we call twisted homology and cohomology. This definition generalises the Thom spectrum of a spherical fibration. We explore this construction through examples and calculations.