A supermanifold is a generalization of the concept of manifold. It consists of a manifold whose local charts contain two types of variables: commuting variables (as in any ordinary manifold) as well as anti-commuting variables.

# Questions tagged [supermanifolds]

6 questions

**19**

votes

**3**answers

### Geometric meaning of Berezin integration

Berezin integration in a Grassmann algebra is defined such that its algebraic properties are analogous to definite integration of ordinary functions: linearity (taking anticommutativity into account), scale invariance and independence from the…

pregunton

- 4,601
- 1
- 22
- 50

**3**

votes

**0**answers

### Intuition for the need of generalizing from mappings to morphisms to functors in supermathematics?

I am currently reading this paper about the categorical formulation of superalgebras and supergeometry, where in definition 2.3 it says that to change the parity of a right supermodule a morphism will not do the job as morphisms have to preserve…

Dilaton

- 1,117
- 11
- 27

**3**

votes

**0**answers

### What exactly is the role of the mysterious space underlying the definition of a superspace?

In the intro to chapter 12.3 of this book about the applications of coherent states, it says that
classical spaces for bosons are real or complex vector spaces or manifolds, whereas classical spaces for fermions are Grassmann algebras…

Dilaton

- 1,117
- 11
- 27

**3**

votes

**0**answers

### What is the geometric significance of the definition of supermanifold?

We know that a supermanifold $M$ is a locally ringed space $(M,O_M)$ which is locally isomorphic to $(U, C^\infty(U) \otimes \wedge W^\ast)$, where $U$ is an open subset of $\mathbb{R}^n$, $W$ is a finite dimensional real vector space and the above…

Soutrik

- 31
- 2

**1**

vote

**0**answers

### Understanding Moonshine and Heterotic E8xE8

Recently I have become familiar with the conjectured relationship of monstrous moonshine and pure $(2+1)$-dimensional quantum gravity in AdS with maximally negative cosmological constant and, it’s being dual to $c=24$ (if I recall) homomorphic…

alex sharma

- 23
- 5

**0**

votes

**1**answer

### Defining supermanifolds by equations

I would like to in what sense supermanifolds may be defined by systems of equations in the ordinary flat superspace. I am particularly interested in the approach to supergeometry via ringed spaces.
Remark: situation is quite clear for me in the case…

Blazej

- 2,703
- 15
- 29