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LSpice
LSpice
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First cohomology of the space of long knots in R^4ℝ⁴

Let's consider the space of long knots in $\mathbb R^n, n>3$$\mathbb R^n$, $n>3$. I know that there are many results (Vassiliev, Turchin, Sinha, Kontsevich) about different expressions of cohomology of this space. I think the last result is about convergency in $E^1$ term (http://palmer.wellesley.edu/~ivolic/pdf/Papers/VassilievCollapseFinalLambrechts, Turchin, and Volić -G%26T.pdf The rational homology of spaces of long knots in codimension $> 2$).

But my question is about what these cohomologies are precise. So, is it true that $H^1(long\ knots\ in\ \mathbb R^4)=0$ $H^1(\text{long knots in $\mathbb R^4$})=0$?

Does there exist some table with $H^i(space\ of\ long\ knots\ in\ \mathbb R^j)$$H^i(\text{space of long knots in $\mathbb R^j$})$ at least for small $i,j$$i$, $j$?

First cohomology of the space of long knots in R^4

Let's consider the space of long knots in $\mathbb R^n, n>3$. I know that there are many results (Vassiliev, Turchin, Sinha, Kontsevich) about different expressions of cohomology of this space. I think the last result is about convergency in $E^1$ term (http://palmer.wellesley.edu/~ivolic/pdf/Papers/VassilievCollapseFinal-G%26T.pdf).

But my question is about what these cohomologies are precise. So, is it true that $H^1(long\ knots\ in\ \mathbb R^4)=0$ ?

Does there exist some table with $H^i(space\ of\ long\ knots\ in\ \mathbb R^j)$ at least for small $i,j$ ?

First cohomology of the space of long knots in ℝ⁴

Let's consider the space of long knots in $\mathbb R^n$, $n>3$. I know that there are many results (Vassiliev, Turchin, Sinha, Kontsevich) about different expressions of cohomology of this space. I think the last result is about convergency in $E^1$ term (Lambrechts, Turchin, and Volić - The rational homology of spaces of long knots in codimension $> 2$).

But my question is about what these cohomologies are precise. So, is it true that $H^1(\text{long knots in $\mathbb R^4$})=0$?

Does there exist some table with $H^i(\text{space of long knots in $\mathbb R^j$})$ at least for small $i$, $j$?

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Dmitri Pavlov
Dmitri Pavlov
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$H^1(space\ of\ long\ knots\ in\ \mathbb First cohomology of the space of long knots in R^4)$

added 11 characters in body; edited title
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Nikita Kalinin
Nikita Kalinin
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$H^1(long\space\ of\ long\ knots\ in\ \mathbb R^4)$

Let's consider the space of long knots in $\mathbb R^n, n>3$. I know that there are many results (Vassiliev, Turchin, Sinha, Kontsevich) about different expressions of cohomology of this space. I think the last result is about convergency in $E^1$ term (http://palmer.wellesley.edu/~ivolic/pdf/Papers/VassilievCollapseFinal-G%26T.pdf).

But my question is about what these cohomologies are precise. So, is it true that $H^1(long\ knots\ in\ \mathbb R^4)=0$ ?

Does there exist some table with $H^i(long\ knots\ in\ \mathbb R^j)$$H^i(space\ of\ long\ knots\ in\ \mathbb R^j)$ at least for small $i,j$ ?

$H^1(long\ knots\ in\ \mathbb R^4)$

Let's consider the space of long knots in $\mathbb R^n, n>3$. I know that there are many results (Vassiliev, Turchin, Sinha, Kontsevich) about different expressions of cohomology of this space. I think the last result is about convergency in $E^1$ term (http://palmer.wellesley.edu/~ivolic/pdf/Papers/VassilievCollapseFinal-G%26T.pdf).

But my question is about what these cohomologies are precise. So, is it true that $H^1(long\ knots\ in\ \mathbb R^4)=0$ ?

Does there exist some table with $H^i(long\ knots\ in\ \mathbb R^j)$ at least for small $i,j$ ?

$H^1(space\ of\ long\ knots\ in\ \mathbb R^4)$

Let's consider the space of long knots in $\mathbb R^n, n>3$. I know that there are many results (Vassiliev, Turchin, Sinha, Kontsevich) about different expressions of cohomology of this space. I think the last result is about convergency in $E^1$ term (http://palmer.wellesley.edu/~ivolic/pdf/Papers/VassilievCollapseFinal-G%26T.pdf).

But my question is about what these cohomologies are precise. So, is it true that $H^1(long\ knots\ in\ \mathbb R^4)=0$ ?

Does there exist some table with $H^i(space\ of\ long\ knots\ in\ \mathbb R^j)$ at least for small $i,j$ ?

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Nikita Kalinin
Nikita Kalinin
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