Arrowtic K-Theory

Welcome to the website of Satya Mandal (the author), a versatile math professor and author at the University of Kansas. Here, you will find a variety of resources to explore his research interest, publications, his courses and his views on the state of academic affairs. 

 

This is, in deed,  a reincarnation of the site mandal.ku.edu that used to be housed by his employer, the  University of Kansas (KU). As a personally owned site, this site is expected to reflect the personality and other aspects of his ownself including but not limited to, his cynicisms, mistrust of the establishment, humor and like things; free from the institutional and governmental guidance. A touch of activism, within the bounds of academic arena, is among the aspirations. Title of the site indicates, K-Theory would be one of the core interest of this site, for now. Long term aspirations and goals would unfold.  

 

By K-Theory we mean Algebraic K-Theory. K-Theory, and its ownership, is a serious business among the practitioners of the same. However, K-Theory means different things to different researchers. In his early career, this author used to specialize in Classical K-Theory and projective modules. More recently, the author’s interest has shifted to Quillen K-Theory.  Arrowtic K-Theory could justifiably be another name to Quillen K-Theory (It rhymes with arithmatic and any other-tic). Arrows are the most fundamental building blocks (the atoms) of Quillen K-Theory. The author names his brand of K-Theory as Arrowtic K-Theory.

 

Experts pointed out to the author that Quillen K-Theory is considered “old fashioned” now, and no-one is working on this any more. The author respects the expert opinion. However, the expert opinion also indicates that this author remains the only active practitioner of Quillen K-Theory now, notwithstanding that this may be contested by other stakeholders outside the beltway. That being the case, the author is entitled to relabel and claim the ownership of Arrowtic K-Theory. This author would like to hear from those who contests this ownership claim, and be happy to share the glory with them, in this blog and otherwise. 

 

Further, tt was pointed out by the experts, that Motivic homotopy theory and motivic cohomology theory form the modern face of algebraic K-theory. Again, with due respect, why not call the motivic stuff whatever that is? It seems deceptive that the motivic stuff will be called K-Theory. There is only a thin connection between Motivic theory and Algebraic K-Theory, as we knew it in the last century. Only common denominator is that Daniel Quillen provided the foundation for both Motivic Theory (model categories) and Higher Algebraic K-Theory. However, it is their choice how they want to label what they practice. Clearly, Algebraic K-Theory is more sellable. Experts are mostly doing homotopy theory, while they call themselves K-theorists. 

 

Arrowtic K-Theory uses commutative algebra tools to interpret Quillen K-Theory. This author tossed the slogan: “We do Algebra without apology”. That is how we approach Arrowtic K-Theory. Arrowtic K-Theory is an attempt to keep Algebraic K-Theory within the fold of Commutative Algebra, as it used to be in the last century.