Lecture notes on trisections and cohomology

نویسندگان

چکیده

In these notes, we describe several geometric interpretations of $H^2(X)$ when $X$ is a trisected 4-manifold. The main insight that, by analogy with Hodge theory and sheaf cohomology in algebraic geometry, classes can be usefully interpeted as $(1,1)$-classes. These notes formed the first half an aborted seminar on symplectic trisections at Max Planck Institute for Mathematics during Spring 2020.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Lecture Notes on Quantum Cohomology of the Flag Manifold

This is an exposition of some recent developments related to the object in the title, particularly the computation of the Gromov-Witten invariants of the flag manifold [5] and the quadratic algebra approach [6]. The notes are largely based on the papers [5] and [6], authored jointly with S. Gelfand, A. N. Kirillov, and A. Postnikov. This is by no means an exhaustive survey of the subject, but r...

متن کامل

18.785F17 Number Theory I Lecture 23 Notes: Tate Cohomology

In this lecture we introduce a variant of group cohomology known as Tate cohomology, and we define the Herbrand quotient (a ratio of cardinalities of two Tate cohomology groups), which will play a key role in our proof of Artin reciprocity. We begin with a brief review of group cohomology, restricting our attention to the minimum we need to define the Tate cohomology groups we will use. At a nu...

متن کامل

Lecture Notes for Course 88-909 Cohomology of Groups

Before starting, we’ll say a few words of motivation. We wish to understand the infinite Galois groupG = Gal(Q/Q), which is very important in number theory. In particular, we wish to understand G-modules, namely modules over some ring that are endowed with an action of G. Such objects tend to be complicated. Recall that in algebraic topology, we define the homology and cohomology of simplicial ...

متن کامل

Notes on Étale Cohomology

à 4.0 Short Comment on Sheaves, Bundles, and Representable Functors. The notion of a sheaf over a topological space X generalize that of a bundle over X . We're more-or-less aware of this. I want to spend some time looking the specifics of this generalization. I'll focus on schemes. Fix a ring A and let 1 :=A 1 be the affine line. The first thing I want to point out is that the global section...

متن کامل

Notes on Étale Cohomology

These notes outline the “fundamental theorems” of étale cohomology, following [4, Ch. vi], as well as briefly discuss the Weil conjectures.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: The open book series

سال: 2022

ISSN: ['2329-9061', '2329-907X']

DOI: https://doi.org/10.2140/obs.2022.5.245