## Tagged Questions

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### complex Morse function on a four-manifold

If we have a complex Morse function on a complex four-manifold, $f: X\to \mathbb{C}$, can we tell from the function how the genus of inverse images $f^{-1}(z)$ (for regular values …
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### Stein manifolds definiton

There are a few equivalent definitions of Stein manifolds. As far as I know they were initially defined as holomorphically convex complex manifolds, and then the other definitions …
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### Affine varieties as Stein surfaces

I have a somewhat general and vague question in mind. Is there anything in literature related to Affine varieties as examples of Stein manifolds? I know that there is a topological …
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### Gluck twist on four-manifolds

I have a basic question which I am not able to figure out. If we do a Gluck twist on a nullhomologous 2-sphere in a 4-manifold, it is said that it does not change its intersection …
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### What is topological surgery conjecture?

I'm a novice in the surgery theory, and I'm encountering the word "(4-dimensional) topological surgery conjecture", which I can't not find the definition. Could anyone help me?
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### What is the state of the art in 4-manfold 2-types?

In an old answer to an old question of mine, Peter Teichner commented that it is an open problem to determine which homotopy 2-types arise from 4-manifolds. In some instances we kn …
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### Almost parallelizable 4-manifolds

On the first page of Milnor-Kervaire's paper "Bernoulli numbers, homotopy groups, and a theorem of Rohlin", they assert without proof or reference that if $M$ is a compact connecte …
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### Intersection form on quotient manifold

Let $E_{1},E_{2}$ be elliptic curves over $\mathbb{C}$. We denote by $\iota_{i}$ the translation by a 2-torsion point on $E_{i}$. Then $G=\mathbb{Z}/2\mathbb{Z}$ acts freely on the …
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### Group action on spin^c 4-manifold.

 I'll try to be more precise. In paper N.Nakamura, "Bauerâ€“Furuta invariants under $Z_2$-actions" there is an assumption that $Z_2$ action "lifts to spin^c structure". What i …
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Question 1. Let $X_i$ be an infinite family of closed, orientable, smooth 4-manifolds with the following properties: a) $\pi_1(X_i) = \mathbb{Z}\times \mathbb{Z_{2}}$ for any $i = … 0answers 168 views ### Shortest Casson tower containing a slice disk for the attaching curve A Casson tower is obtained as follows: Start with a properly immersed disk in$\mathbb{B}^4\$ - a regular neighborhood of such a disk is called a kinky handle. The boundary of the c …

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