The study successfully computes THH (E2) and relates it to K(i)-homology classes.
Abstract The Morava E -theories, E₍ E n, are complex-oriented 2-periodic ring spectra, with homotopy groups W{ {₅}^₍}[u₁, u₂, , u₍-₁]u, u^-1 W F p n [ u 1, u 2, …, u n - 1 ] u, u - 1. Here W denotes the ring of Witt vectors. E₍ E n is a Landweber exact spectrum and hence uniquely determined by its homotopy groups as BP* B P ∗ -algebra. Algebraic K -theory of E₍ E n is a key ingredient towards analyzing the layers in the p -complete Waldhausen’s algebraic K -theory chromatic tower. One hopes to use the machinery of trace methods to get results towards algebraic K -theory once the computation for THH (E₍) T H H (E n) is known. In this paper we describe THH (E₂) T H H (E 2) as part of consecutive chain of cofiber sequences where each cofiber sits in the next cofiber sequence and the first term of each cofiber sequence is describable completely in terms of suspensions and localizations of E₂ E 2. For these results, we first calculate K (i) -homology of THH (E₂) T H H (E 2) using a Bökstedt spectral sequence and then lift the generating classes of <j
Sanjana Agarwal (Wed,) conducted a other in Morava E-theory spectrum E2. THH of the Morava E-theory spectrum E2 was evaluated on THH (E2) computations and lifting K(i)-homology classes to π∗THH (E2). The study successfully computes THH (E2) and relates it to K(i)-homology classes.