We study maps from a smooth scheme to a motivic sphere in the Morel–Voevodsky A1-
homotopy category, ie, motivic cohomotopy sets. Following Borsuk, we show that, in the …

Let AA be a commutative Noetherian ring and PP be a projective A A-module of rank=(dim
(A)-1)=(dim (A)-1). An intriguing open question is to find the precise obstruction for PP to split …

Let A be a ring of dimension d containing an infinite field k, T 1,…, T r be variables over A
and P be a projective A [T 1,…, T r]-module of rank n. Assume one of the following conditions …

Let R be a commutative Noetherian ring and R↪ S be a subintegral extension. It is proved
that the top Euler class group of R is isomorphic to the top Euler class group of S. An …

Let A be a commutative noetherian ring, containing a field k, with 1/2∈ k, dim⁡ A= d, and let
P be a projective A-module, with rank (P)= n. Let LO (P) denote the set of all pairs (I, ω) …

In this paper the relative algebraic obstruction groups (also known as Euler class groups)
were defined and some excision exact sequences were established. In particular, for a …

For a projective A-module P, with n= rank (P)≥ 2, the Homotopy obstruction sets π 0 LO (P)
were defined, in, to detect whether P has a free direct summand or not. These sets have a …

In this paper, we give a proof for the isomorphism between the generalized Euler Class
Groups Ed (X; 多) and the Chow-Witt group with line bundle twist CHd (X, 多), for smooth …

In this paper, we construct an action of Picard group on the generalized Euler classes
defined in Chow-Witt groups CH^ d (X, L) CH d (X, L)~ with twisted line bundle LL, which is …

University of Kansas Thesis Template Page 1 Obstruction Theory in Algebra and Topology: A
Homotopy Perspective ©2022 Bibekananda Mishra Submitted to the graduate degree program …